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New developments in the numerical conformal bootstrap

Slava Rychkov and Ning Su

Slava Rychkov

Ning Su

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Rev. Mod. Phys. 96, 045004 – Published 21 November, 2024

DOI: https://doi.org/10.1103/RevModPhys.96.045004

Abstract

Over the past 15 years, the numerical conformal bootstrap has become an indispensable tool for studying strongly coupled conformal field theories in various dimensions. Reviewed here are the main developments in the field in the five years since the publication of the previous comprehensive review [D. Poland, S. Rychkov, and A. Vichi, Rev. Mod. Phys. 91, 015002 (2019)]. Developments in the software (SDPB 2.0, scalar_blocks, blocks_3d, autoboot, hyperion, and simpleboot) and on the algorithmic side (Delaunay triangulation, cutting surface, tiptop, navigator function, and skydive) are described. Also chronicled are the main physics applications that have been obtained using new technologies.

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References (211)

  1. Afkhami-Jeddi, Nima, 2022, “Conformal bootstrap deformations,” J. High Energy Phys. 09, 225.
  2. Afkhami-Jeddi, Nima, Henry Cohn, Thomas Hartman, David de Laat, and Amirhossein Tajdini, 2020, “High-dimensional sphere packing and the modular bootstrap,” J. High Energy Phys. 12, 066.
  3. Afkhami-Jeddi, Nima, Thomas Hartman, and Amirhossein Tajdini, 2019, “Fast conformal bootstrap and constraints on 3d gravity,” J. High Energy Phys. 05, 087.
  4. Agmon, Nathan B., Shai M. Chester, and Silviu S. Pufu, 2020, “The M-theory archipelago,” J. High Energy Phys. 02, 010.
  5. Aharony, A., O. Entin-Wohlman, and A. Kudlis, 2022, “Different critical behaviors in cubic to trigonal and tetragonal perovskites,” Phys. Rev. B 105, 104101.
  6. Aharony, Amnon, 1973, “Critical behavior of anisotropic cubic systems,” Phys. Rev. B 8, 4270–4273.
  7. Aharony, Ofer, Steven S. Gubser, Juan Martin Maldacena, Hirosi Ooguri, and Yaron Oz, 2000, “Large N field theories, string theory and gravity,” Phys. Rep. 323, 183–386.
  8. Albayrak, Soner, Rajeev S. Erramilli, Zhijin Li, David Poland, and Yuan Xin, 2022, “Bootstrapping Nf=4 conformal QED3,” Phys. Rev. D 105, 085008.
  9. Anderson, Peter D., and Martin Kruczenski, 2017, “Loop equations and bootstrap methods in the lattice,” Nucl. Phys. B921, 702–726.
  10. Atanasov, Alexander, Aaron Hillman, and David Poland, 2018, “Bootstrapping the minimal 3D SCFT,” J. High Energy Phys. 11 140.
  11. Atanasov, Alexander, Aaron Hillman, David Poland, Junchen Rong, and Ning Su, 2022, “Precision bootstrap for the N=1 super-Ising model,” J. High Energy Phys. 08, 136.
  12. Bae, Jin-Beom, 2019, “Constraining two dimensional CFTs with modular invariance,” Proc. Sci. ICHEP2018, 318.
  13. Bae, Jin-Beom, Sungjay Lee, and Jaewon Song, 2019, “Modular constraints on superconformal field theories,” J. High Energy Phys. 01, 209.
  14. Bashkirov, Denis, 2013, “Bootstrapping the N=1 SCFT in three dimensions,” arXiv:1310.8255.
  15. Behan, Connor, 2017, “PyCFTBoot: A flexible interface for the conformal bootstrap,” Commun. Comput. Phys. 22, 1–38.
  16. Behan, Connor, 2018, “Conformal manifolds: ODEs from OPEs,” J. High Energy Phys. 03, 127.
  17. Behan, Connor, 2019, “Bootstrapping the long-range Ising model in three dimensions,” J. Phys. A 52, 075401.
  18. Behan, Connor, Lorenzo Di Pietro, Edoardo Lauria, and Balt C. van Rees, 2020, “Bootstrapping boundary-localized interactions,” J. High Energy Phys. 12, 182.
  19. Behan, Connor, Lorenzo Di Pietro, Edoardo Lauria, and Balt C. van Rees, 2022, “Bootstrapping boundary-localized interactions II. Minimal models at the boundary,” J. High Energy Phys. 03, 146.
  20. Behan, Connor, Peter Kravchuk, Walter Landry, and David Simmons-Duffin, 2019, computer code scalar_blocks, https://gitlab.com/bootstrapcollaboration/scalar_blocks.
  21. Behan, Connor, Edoardo Lauria, Maria Nocchi, and Philine van Vliet, 2023, “Analytic and numerical bootstrap for the long-range Ising model,” arXiv:2311.02742.
  22. Belavin, A. A., Alexander M. Polyakov, and A. B. Zamolodchikov, 1984, “Infinite conformal symmetry in two-dimensional quantum field theory,” Nucl. Phys. B241, 333–380.
  23. Benjamin, Nathan, and Cyuan-Han Chang, 2022, “Scalar modular bootstrap and zeros of the Riemann zeta function,” J. High Energy Phys. 11, 143.
  24. Benjamin, Nathan, and Ying-Hsuan Lin, 2020, “Lessons from the Ramond sector,” SciPost Phys. 9, 065.
  25. Binder, Damon J., Shai M. Chester, Max Jerdee, and Silviu S. Pufu, 2021, “The 3d N=6 bootstrap: From higher spins to strings to membranes,” J. High Energy Phys. 05, 083.
  26. Bissi, Agnese, Francesco Fucito, Andrea Manenti, José Francisco Morales, and Raffaele Savelli, 2022, “OPE coefficients in Argyres-Douglas theories,” J. High Energy Phys. 06, 085.
  27. Bissi, Agnese, Andrea Manenti, and Alessandro Vichi, 2021, “Bootstrapping mixed correlators in N=4 super Yang-Mills,” J. High Energy Phys. 05, 111.
  28. Bissi, Agnese, Aninda Sinha, and Xinan Zhou, 2022, “Selected topics in analytic conformal bootstrap: A guided journey,” Phys. Rep. 991, 1–89.
  29. Bonanno, Claudio, Andrea Cappelli, Mikhail Kompaniets, Satoshi Okuda, and Kay Jörg Wiese, 2023, “Benchmarking the Ising universality class in 3≤d<4 dimensions,” SciPost Phys. 14, 135.
  30. Bonifacio, James, 2022a, “Bootstrap bounds on closed hyperbolic manifolds,” J. High Energy Phys. 02, 025.
  31. Bonifacio, James, 2022b, “Bootstrapping closed hyperbolic surfaces,” J. High Energy Phys. 03, 093.
  32. Bonifacio, James, and Kurt Hinterbichler, 2020, “Bootstrap bounds on closed Einstein manifolds,” J. High Energy Phys. 10, 069.
  33. Bonifacio, James, Dalimil Mazac, and Sridip Pal, 2023, “Spectral bounds on hyperbolic 3-manifolds: Associativity and the trace formula,” arXiv:2308.11174.
  34. Cappelli, Andrea, Lorenzo Maffi, and Satoshi Okuda, 2019, “Critical Ising model in varying dimension by conformal bootstrap,” J. High Energy Phys. 01, 161.
  35. Cardy, John L., 1987, “Conformal invariance,” in Phase Transitions and Critical Phenomena, Vol. 11, edited by C. M. Domb and M. S. Green (Academic Press, New York), pp. 55–126.
  36. Cavaglià, Andrea, Nikolay Gromov, Julius Julius, and Michelangelo Preti, 2022a, “Bootstrability in defect CFT: Integrated correlators and sharper bounds,” J. High Energy Phys. 05, 164.
  37. Cavaglià, Andrea, Nikolay Gromov, Julius Julius, and Michelangelo Preti, 2022b, “Integrability and conformal bootstrap: One dimensional defect conformal field theory,” Phys. Rev. D 105, L021902.
  38. Chen, Bin-Bin, Xu Zhang, and Zi Yang Meng, 2024, “Emergent conformal symmetry at the multicritical point of (2+1)D SO(5) model with Wess-Zumino-Witten term on sphere,” arXiv:2405.04470.
  39. Chen, Bin-Bin, Xu Zhang, Yuxuan Wang, Kai Sun, and Zi Yang Meng, 2023, “Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: Multicritical point and disorder phase,” arXiv:2307.05307.
  40. Chester, Shai M., 2023, “Bootstrapping 4d N=2 gauge theories: The case of SQCD,” J. High Energy Phys. 01, 107.
  41. Chester, Shai M., Ross Dempsey, and Silviu S. Pufu, 2023, “Bootstrapping N=4 super-Yang-Mills on the conformal manifold,” J. High Energy Phys. 01, 038.
  42. Chester, Shai M., Luca V. Iliesiu, Mark Mezei, and Silviu S. Pufu, 2018, “Monopole operators in U(1) Chern-Simons-Matter theories,” J. High Energy Phys. 05, 157.
  43. Chester, Shai M., Walter Landry, Junyu Liu, David Poland, David Simmons-Duffin, Ning Su, and Alessandro Vichi, 2021, “Bootstrapping Heisenberg magnets and their cubic instability,” Phys. Rev. D 104, 105013.
  44. Chester, Shai M., Walter Landry, Junyu Liu, David Poland, David Simmons-Duffin, Ning Su, and Alessandro Vichi, 2020, “Carving out OPE space and precise O(2) model critical exponents,” J. High Energy Phys. 06, 142.
  45. Chester, Shai M., and Silviu S. Pufu, 2016, “Towards bootstrapping QED3,” J. High Energy Phys. 08, 019.
  46. Chester, Shai M., and Ning Su, 2022, “Upper critical dimension of the 3-state Potts model,” arXiv:2210.09091.
  47. Chester, Shai M., and Ning Su, 2024, “Bootstrapping Deconfined Quantum Tricriticality,” Phys. Rev. Lett. 132, 111601.
  48. Chiang, Li-Yuan, Tzu-Chen Huang, Yu-tin Huang, Wei Li, Laurentiu Rodina, and He-Chen Weng, 2023, “The geometry of the modular bootstrap,” arXiv:2308.11692.
  49. Cho, Minjae, Barak Gabai, Ying-Hsuan Lin, Victor A. Rodriguez, Joshua Sandor, and Xi Yin, 2022, “Bootstrapping the Ising model on the lattice,” arXiv:2206.12538.
  50. Collier, Scott, Dalimil Mazac, and Yifan Wang, 2023, “Bootstrapping boundaries and branes,” J. High Energy Phys. 02, 019.
  51. Douglas, Michael R., 2013, “Spaces of quantum field theories,” J. Phys. Conf. Ser. 462, 012011.
  52. Dymarsky, Anatoly, Joao Penedones, Emilio Trevisani, and Alessandro Vichi, 2019, “Charting the space of 3D CFTs with a continuous global symmetry,” J. High Energy Phys. 05, 098.
  53. El-Showk, Sheer, and Miguel F. Paulos, 2013, “Bootstrapping Conformal Field Theories with the Extremal Functional Method,” Phys. Rev. Lett. 111, 241601.
  54. El-Showk, Sheer, Miguel F. Paulos, David Poland, Slava Rychkov, David Simmons-Duffin, and Alessandro Vichi, 2012, “Solving the 3D Ising model with the conformal bootstrap,” Phys. Rev. D 86, 025022.
  55. El-Showk, Sheer, Miguel F. Paulos, David Poland, Slava Rychkov, David Simmons-Duffin, and Alessandro Vichi, 2014a, “Conformal Field Theories in Fractional Dimensions,” Phys. Rev. Lett. 112, 141601.
  56. El-Showk, Sheer, Miguel F. Paulos, David Poland, Slava Rychkov, David Simmons-Duffin, and Alessandro Vichi, 2014b, “Solving the 3d Ising model with the conformal bootstrap II. c-minimization and precise critical exponents,” J. Stat. Phys. 157, 869.
  57. Erramilli, Rajeev S., Luca V. Iliesiu, and Petr Kravchuk, 2019, “Recursion relation for general 3d blocks,” J. High Energy Phys. 12, 116.
  58. Erramilli, Rajeev S., Luca V. Iliesiu, Petr Kravchuk, Walter Landry, David Poland, and David Simmons-Duffin, 2021, “blocks_3d: Software for general 3d conformal blocks,” J. High Energy Phys. 11, 006.
  59. Erramilli, Rajeev S., Luca V. Iliesiu, Petr Kravchuk, Aike Liu, David Poland, and David Simmons-Duffin, 2023, “The Gross-Neveu-Yukawa archipelago,” J. High Energy Phys. 02, 036.
  60. Fitzpatrick, A. Liam, and Wei Li, 2023, “Improving modular bootstrap bounds with integrality,” arXiv:2308.08725.
  61. Gesteau, Elliott, Sridip Pal, David Simmons-Duffin, and Yixin Xu, 2023, “Bounds on spectral gaps of hyperbolic spin surfaces,” arXiv:2311.13330.
  62. Ghosh, Kausik, Apratim Kaviraj, and Miguel F. Paulos, 2021, “Charging up the functional bootstrap,” J. High Energy Phys. 10, 116.
  63. Ghosh, Kausik, and Zechuan Zheng, 2023, “Numerical conformal bootstrap with analytic functionals and outer approximation,” arXiv:2307.11144.
  64. Gimenez-Grau, Aleix, and Pedro Liendo, 2020, “Bootstrapping line defects in N=2 theories,” J. High Energy Phys. 03, 121.
  65. Gimenez-Grau, Aleix, and Pedro Liendo, 2021, “Bootstrapping Coulomb and Higgs branch operators,” J. High Energy Phys. 01, 175.
  66. Gliozzi, Ferdinando, 2013, “More Constraining Conformal Bootstrap,” Phys. Rev. Lett. 111, 161602.
  67. Go, Mocho, 2020, “An automated generation of bootstrap equations for numerical study of critical phenomena,” arXiv:2006.04173.
  68. Go, Mocho, and Yuji Tachikawa, 2019, “autoboot: A generator of bootstrap equations with global symmetry,” J. High Energy Phys. 06, 084.
  69. Golden, John, and Miguel F. Paulos, 2015, “No unitary bootstrap for the fractal Ising model,” J. High Energy Phys. 03, 167.
  70. Gorbenko, Victor, Slava Rychkov, and Bernardo Zan, 2018a, “Walking, weak first-order transitions, and complex CFTs,” J. High Energy Phys. 10, 108.
  71. Gorbenko, Victor, Slava Rychkov, and Bernardo Zan, 2018b, “Walking, weak first-order transitions, and complex CFTs II. Two-dimensional Potts model at Q>4,” SciPost Phys. 5, 050.
  72. Gracey, J. A., 2018, “Fermion bilinear operator critical exponents at O(1/N2) in the QED-Gross-Neveu universality class,” Phys. Rev. D 98, 085012.
  73. Grans-Samuelsson, Linnea, Rongvoram Nivesvivat, Jesper Lykke Jacobsen, Sylvain Ribault, and Hubert Saleur, 2022, “Global symmetry and conformal bootstrap in the two-dimensional O(n) model,” SciPost Phys. 12, 147.
  74. Grigoletto, Andrea, 2021, “Anomalies of fermionic CFTs via cobordism and bootstrap,” arXiv:2112.01485.
  75. Grigoletto, Andrea, and Pavel Putrov, 2023, “Spin-cobordisms, surgeries and fermionic modular bootstrap,” Commun. Math. Phys. 401, 3169–3245.
  76. Grover, Tarun, D. N. Sheng, and Ashvin Vishwanath, 2014, “Emergent space-time supersymmetry at the boundary of a topological phase,” Science 344, 280–283.
  77. Gukov, Sergei, 2017, “RG flows and bifurcations,” Nucl. Phys. B919, 583–638.
  78. Han, Xizhi, Sean A. Hartnoll, and Jorrit Kruthoff, 2020, “Bootstrapping Matrix Quantum Mechanics,” Phys. Rev. Lett. 125, 041601.
  79. Hartman, Thomas, Dalimil Mazáč, David Simmons-Duffin, and Alexander Zhiboedov, 2022, “Snowmass white paper: The analytic conformal bootstrap,” in Proceedings of the 2021 U.S. Community Study on the Future of Particle Physics (Snowmass 2021), 2021, edited by Joel N. Butler, R. Sekhar Chivukula, and Michael E. Peskin, https://www.slac.stanford.edu/econf/C210711/.
  80. Hartman, Thomas, Dalimil Mazáč, and Leonardo Rastelli, 2019, “Sphere packing and quantum gravity,” J. High Energy Phys. 12, 048.
  81. Hasenbusch, Martin, 2019, “Monte Carlo study of an improved clock model in three dimensions,” Phys. Rev. B 100, 224517.
  82. Hasenbusch, Martin, 2023, “Cubic fixed point in three dimensions: Monte Carlo simulations of the ϕ4 model on the simple cubic lattice,” Phys. Rev. B 107, 024409.
  83. Hasenbusch, Martin, and Ettore Vicari, 2011, “Anisotropic perturbations in three-dimensional O(N)-symmetric vector models,” Phys. Rev. B 84, 125136.
  84. He, Yin-Chen, Junchen Rong, and Ning Su, 2021a, “A roadmap for bootstrapping critical gauge theories: Decoupling operators of conformal field theories in d>2 dimensions,” SciPost Phys. 11, 111.
  85. He, Yin-Chen, Junchen Rong, and Ning Su, 2021b, “Non-Wilson-Fisher kinks of O(N) numerical bootstrap: From the deconfined phase transition to a putative new family of CFTs,” SciPost Phys. 10, 115.
  86. He, Yin-Chen, Junchen Rong, and Ning Su, 2022, “Conformal bootstrap bounds for the U(1) Dirac spin liquid and N=7 Stiefel liquid,” SciPost Phys. 13, 014.
  87. He, Yin-Chen, Junchen Rong, Ning Su, and Alessandro Vichi, 2023, “Non-Abelian currents bootstrap,” arXiv:2302.11585.
  88. He, Yin-Chen, Michael P. Zaletel, Masaki Oshikawa, and Frank Pollmann, 2017, “Signatures of Dirac Cones in a DMRG Study of the Kagome Heisenberg Model,” Phys. Rev. X 7, 031020.
  89. Hellerman, Simeon, Domenico Orlando, Susanne Reffert, and Masataka Watanabe, 2015, “On the CFT operator spectrum at large global charge,” J. High Energy Phys. 12, 071.
  90. Henriksson, Johan, Stefanos R. Kousvos, and Marten Reehorst, 2023, “Spectrum continuity and level repulsion: The Ising CFT from infinitesimal to finite ϵ,” J. High Energy Phys. 02, 218.
  91. Henriksson, Johan, Stefanos Robert Kousvos, and Andreas Stergiou, 2020, “Analytic and numerical bootstrap of CFTs with O(m)×O(n) global symmetry in 3D,” SciPost Phys. 9, 035.
  92. Henriksson, Johan, and Andreas Stergiou, 2021, “Perturbative and nonperturbative studies of CFTs with MN global symmetry,” SciPost Phys. 11, 015.
  93. Hermele, Michael, T. Senthil, and Matthew P. A. Fisher, 2005, “Algebraic spin liquid as the mother of many competing orders,” Phys. Rev. B 72, 104404.
  94. Hofman, Diego M., and Juan Maldacena, 2008, “Conformal collider physics: Energy and charge correlations,” J. High Energy Phys. 05, 012.
  95. Hogervorst, Matthijs, Slava Rychkov, and Balt C. van Rees, 2015, “Truncated conformal space approach in d dimensions: A cheap alternative to lattice field theory?” Phys. Rev. D 91, 025005.
  96. Hogervorst, Matthijs, Slava Rychkov, and Balt C. van Rees, 2016, “Unitarity violation at the Wilson-Fisher fixed point in 4-ε dimensions,” Phys. Rev. D 93, 125025.
  97. Hu, Shijie, W. Zhu, Sebastian Eggert, and Yin-Chen He, 2019, “Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet,” Phys. Rev. Lett. 123, 207203.
  98. Huang, Yu-Tin, Wei Li, and Guan-Lin Lin, 2019, “The geometry of optimal functionals,” arXiv:1912.01273.
  99. Huffman, Emilie, and Shailesh Chandrasekharan, 2020, “Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality,” Phys. Rev. D 101, 074501.
  100. Ihrig, Bernhard, Luminita N. Mihaila, and Michael M. Scherer, 2018, “Critical behavior of Dirac fermions from perturbative renormalization,” Phys. Rev. B 98, 125109.
  101. Iliesiu, Luca, 2018, “Bootstrapping the Néel-VBS quantum phase transition,” lecture, Simons Center for Geometry and Physics.
  102. Iliesiu, Luca, Filip Kos, David Poland, Silviu S. Pufu, David Simmons-Duffin, and Ran Yacoby, 2016, “Bootstrapping 3D fermions,” J. High Energy Phys. 03, 120.
  103. Janke, Wolfhard, and Ramon Villanova, 1997, “Three-dimensional three state Potts model revisited with new techniques,” Nucl. Phys. B489, 679–696.
  104. Kadanoff, Leo P., 1969, “Operator Algebra and the Determination of Critical Indices,” Phys. Rev. Lett. 23, 1430–1433.
  105. Kántor, Gergely, Vasilis Niarchos, and Constantinos Papageorgakis, 2022, “Conformal bootstrap with reinforcement learning,” Phys. Rev. D 105, 025018.
  106. Karthik, Nikhil, and Rajamani Narayanan, 2016a, “No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions,” Phys. Rev. D 93, 045020.
  107. Karthik, Nikhil, and Rajamani Narayanan, 2016b, “Scale invariance of parity-invariant three-dimensional QED,” Phys. Rev. D 94, 065026.
  108. Karthik, Nikhil, and Rajamani Narayanan, 2019, “Numerical determination of monopole scaling dimension in parity-invariant three-dimensional noncompact QED,” Phys. Rev. D 100, 054514.
  109. Kazakov, Vladimir, and Zechuan Zheng, 2022, “Analytic and numerical bootstrap for one-matrix model and ‘unsolvable’ two-matrix model,” J. High Energy Phys. 06, 030.
  110. Kazakov, Vladimir, and Zechuan Zheng, 2023, “Bootstrap for lattice Yang-Mills theory,” Phys. Rev. D 107, L051501.
  111. Korchemsky, G. P., 2016, “On level crossing in conformal field theories,” J. High Energy Phys. 03, 212.
  112. Kos, Filip, David Poland, and David Simmons-Duffin, 2014a, “Bootstrapping mixed correlators in the 3D Ising model,” J. High Energy Phys. 11, 109.
  113. Kos, Filip, David Poland, and David Simmons-Duffin, 2014b, “Bootstrapping the O(N) vector models,” J. High Energy Phys. 06, 091.
  114. Kos, Filip, David Poland, David Simmons-Duffin, and Alessandro Vichi, 2015, “Bootstrapping the O(N) Archipelago,” J. High Energy Phys. 11, 106.
  115. Kos, Filip, David Poland, David Simmons-Duffin, and Alessandro Vichi, 2016, “Precision islands in the Ising and O(N) models,” J. High Energy Phys. 08, 036.
  116. Kousvos, Stefanos R., and Andreas Stergiou, 2019, “Bootstrapping mixed correlators in three-dimensional cubic theories,” SciPost Phys. 6, 035.
  117. Kousvos, Stefanos R., and Andreas Stergiou, 2020, “Bootstrapping mixed correlators in three-dimensional cubic theories II,” SciPost Phys. 8, 085.
  118. Kousvos, Stefanos Robert, and Andreas Stergiou, 2022, “Bootstrapping mixed MN correlators in 3D,” SciPost Phys. 12, 206.
  119. Kousvos, Stefanos Robert, and Andreas Stergiou, 2023, “CFTs with U(m)×U(n) global symmetry in 3D and the chiral phase transition of QCD,” SciPost Phys. 15, 075.
  120. Kravchuk, Petr, Dalimil Mazac, and Sridip Pal, 2021, “Automorphic spectra and the conformal bootstrap,” arXiv:2111.12716.
  121. Kruczenski, Martin, Joao Penedones, and Balt C. van Rees, 2022, “Snowmass white paper: S-matrix bootstrap,” arXiv:2203.02421.
  122. Laio, Alessandro, Uriel Luviano Valenzuela, and Marco Serone, 2022, “Monte Carlo approach to the conformal bootstrap,” Phys. Rev. D 106, 025019.
  123. Lal, Shailesh, Suvajit Majumder, and Evgeny Sobko, 2023, “The R-mAtrIx net,” arXiv:2304.07247.
  124. Landry, Walter, 2022, computer code outer_limits, https://github.com/davidsd/sdpb/tree/2.5.0/src/outer_limits.
  125. Landry, Walter, and David Simmons-Duffin, 2019, “Scaling the semidefinite program solver SDPB,” arXiv:1909.09745.
  126. Lanzetta, Ryan A., and Lukasz Fidkowski, 2023, “Bootstrapping Lieb-Schultz-Mattis anomalies,” Phys. Rev. B 107, 205137.
  127. Lee, Jooyoung, and J. M. Kosterlitz, 1991, “Three-dimensional q-state Potts model: Monte Carlo study near q=3,” Phys. Rev. B 43, 1268–1271.
  128. Li, Zhijin, 2022a, “Bootstrapping conformal QED3 and deconfined quantum critical point,” J. High Energy Phys. 11, 005.
  129. Li, Zhijin, 2022b, “Conformality and self-duality of Nf=2 QED3,” Phys. Lett. B 831, 137192.
  130. Li, Zhijin, and David Poland, 2021, “Searching for gauge theories with the conformal bootstrap,” J. High Energy Phys. 03, 172.
  131. Liendo, Pedro, Carlo Meneghelli, and Vladimir Mitev, 2018, “Bootstrapping the half-BPS line defect,” J. High Energy Phys. 10, 077.
  132. Lin, Henry W., 2020, “Bootstraps to strings: Solving random matrix models with positivity,” J. High Energy Phys. 06, 090.
  133. Lin, Henry W., 2023, “Bootstrap bounds on D0-brane quantum mechanics,” J. High Energy Phys. 06, 038.
  134. Lin, Ying-Hsuan, David Meltzer, Shu-Heng Shao, and Andreas Stergiou, 2019, “Bounds on triangle anomalies in (3+1)d,” arXiv:1909.11676.
  135. Lin, Ying-Hsuan, and Shu-Heng Shao, 2019, “Anomalies and bounds on charged operators,” Phys. Rev. D 100, 025013.
  136. Lin, Ying-Hsuan, and Shu-Heng Shao, 2021, “ZN symmetries, anomalies, and the modular bootstrap,” Phys. Rev. D 103, 125001.
  137. Lin, Ying-Hsuan, and Shu-Heng Shao, 2023, “Bootstrapping noninvertible symmetries,” Phys. Rev. D 107, 125025.
  138. Lipa, J. A., J. A. Nissen, D. A. Stricker, D. R. Swanson, and T. C. P. Chui, 2003, “Specific heat of liquid helium in zero gravity very near the lambda point,” Phys. Rev. B 68, 174518.
  139. Lipa, J. A., D. R. Swanson, J. A. Nissen, T. C. P. Chui, and U. E. Israelsson, 1996, “Heat Capacity and Thermal Relaxation of Bulk Helium very near the Lambda Point,” Phys. Rev. Lett. 76, 944–947.
  140. Lipa, J. A., D. R. Swanson, J. A. Nissen, Z. K. Geng, P. R. Williamson, D. A. Stricker, T. C. P. Chui, U. E. Israelsson, and M. Larson, 2000, “Specific Heat of Helium Confined to a 57−μm Planar Geometry near the Lambda Point,” Phys. Rev. Lett. 84, 4894–4897.
  141. Liu, Aike, David Simmons-Duffin, Ning Su, and Balt C. van Rees, 2023, “Skydiving to bootstrap islands,” arXiv:2307.13046.
  142. Liu, Junyu, David Meltzer, David Poland, and David Simmons-Duffin, 2020, “The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT,” J. High Energy Phys. 09, 115; 01 (2021) 206(E).
  143. Liu, Yuzhi, Wei Wang, Kai Sun, and Zi Yang Meng, 2020, “Designer Monte Carlo simulation for the Gross-Neveu-Yukawa transition,” Phys. Rev. B 101, 064308.
  144. Luty, Markus A., and Takemichi Okui, 2006, “Conformal technicolor,” J. High Energy Phys. 09, 070.
  145. Luviano, Valenzuela and Uriel Adrian, 2022, “Stochastic minimization in the conformal bootstrap,” Ph.D. thesis [International School for Advanced Studies (SISSA)].
  146. Ma, Ruochen, and Chong Wang, 2020, “Theory of deconfined pseudocriticality,” Phys. Rev. B 102, 020407.
  147. Maldacena, Juan, and Alexander Zhiboedov, 2013, “Constraining conformal field theories with a higher spin symmetry,” J. Phys. A 46, 214011.
  148. Manashov, Alexander N., and Matthias Strohmaier, 2018, “Correction exponents in the Gross-Neveu-Yukawa model at 1/N2,” Eur. Phys. J. C 78, 454.
  149. Metlitski, Max A., 2022, “Boundary criticality of the O(N) model in d=3 critically revisited,” SciPost Phys. 12, 131.
  150. Mitchell, Matthew S., and David Poland, 2024, “Bounding irrelevant operators in the 3d Gross-Neveu-Yukawa CFTs,” arXiv:2406.12974.
  151. Monin, Alexander, David Pirtskhalava, Riccardo Rattazzi, and Fiona K. Seibold, 2017, “Semiclassics, Goldstone bosons and CFT data,” J. High Energy Phys. 06, 011.
  152. Nahum, Adam, 2020, “Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions,” Phys. Rev. B 102, 201116.
  153. Nakayama, Yu, 2015, “Scale invariance vs conformal invariance,” Phys. Rep. 569, 1–93.
  154. Nakayama, Yu, 2021, “Is there supersymmetric Lee-Yang fixed point in three dimensions?,” Int. J. Mod. Phys. A 36, 2150176.
  155. Nakayama, Yu, and Tomoki Ohtsuki, 2014, “Approaching the conformal window of O(n)×O(m) symmetric Landau-Ginzburg models using the conformal bootstrap,” Phys. Rev. D 89, 126009.
  156. Nakayama, Yu, and Tomoki Ohtsuki, 2016, “Conformal Bootstrap Dashing Hopes of Emergent Symmetry,” Phys. Rev. Lett. 117, 131601.
  157. Niarchos, V., C. Papageorgakis, P. Richmond, A. G. Stapleton, and M. Woolley, 2023, “Bootstrability in line-defect CFT with improved truncation methods,” arXiv:2306.15730.
  158. Nivesvivat, Rongvoram, and Sylvain Ribault, 2021, “Logarithmic CFT at generic central charge: From Liouville theory to the Q-state Potts model,” SciPost Phys. 10, 021.
  159. Ohtsuki, Tomoki, 2016a, computer code cboot, https://github.com/tohtsky/cboot.
  160. Ohtsuki, Tomoki, 2016b, “Applied conformal bootstrap,” Ph.D. thesis (University of Tokyo).
  161. Padayasi, Jaychandran, Abijith Krishnan, Max A. Metlitski, Ilya A. Gruzberg, and Marco Meineri, 2022, “The extraordinary boundary transition in the 3d O(N) model via conformal bootstrap,” SciPost Phys. 12, 190.
  162. Paulos, Miguel F., 2014, “JuliBootS: A hands-on guide to the conformal bootstrap,” arXiv:1412.4127.
  163. Paulos, Miguel F., and Bernardo Zan, 2020, “A functional approach to the numerical conformal bootstrap,” J. High Energy Phys. 09, 006.
  164. Paulos, Miguel F., and Zechuan Zheng, 2022, “Bounding 3d CFT correlators,” J. High Energy Phys. 04, 102.
  165. Pelissetto, Andrea, and Ettore Vicari, 2002, “Critical phenomena and renormalization-group theory,” Phys. Rep. 368, 549–727.
  166. Picco, Marco, Sylvain Ribault, and Raoul Santachiara, 2019, “On four-point connectivities in the critical 2d Potts model,” SciPost Phys. 7, 044.
  167. Poland, David, Valentina Prilepina, and Petar Tadić, 2023, “The five-point bootstrap,” J. High Energy Phys. 10, 153.
  168. Poland, David, Slava Rychkov, and Alessandro Vichi, 2019, “The conformal bootstrap: Theory, numerical techniques, and applications,” Rev. Mod. Phys. 91, 015002.
  169. Poland, David, and David Simmons-Duffin, 2022, “Snowmass white paper: The numerical conformal bootstrap,” in Proceedings of the 2021 U.S. Community Study on the Future of Particle Physics (Snowmass 2021), 2021, edited by Joel N. Butler, R. Sekhar Chivukula, and Michael E. Peskin, https://www.slac.stanford.edu/econf/C210711/.
  170. Polchinski, J., 2007, String Theory. Vol. 1: An Introduction to the Bosonic String (Cambridge University Press, Cambridge, England).
  171. Polyakov, A. M., 1974, “Non-Hamiltonian approach to conformal quantum field theory,” Zh. Eksp. Teor. Fiz. 66, 23–42, https://inspirehep.net/literature/96660.
  172. Qin, Yan Qi, Yuan-Yao He, Yi-Zhuang You, Zhong-Yi Lu, Arnab Sen, Anders W. Sandvik, Cenke Xu, and Zi Yang Meng, 2017, “Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition Phys. Rev. X 7, 031052.
  173. Rattazzi, Riccardo, Vyacheslav S. Rychkov, Erik Tonni, and Alessandro Vichi, 2008, “Bounding scalar operator dimensions in 4D CFT,” J. High Energy Phys. 12, 031.
  174. Reehorst, Marten, 2022, “Rigorous bounds on irrelevant operators in the 3d Ising model CFT,” J. High Energy Phys. 09, 177.
  175. Reehorst, Marten, Maria Refinetti, and Alessandro Vichi, 2023, “Bootstrapping traceless symmetric O(N) scalars,” SciPost Phys. 14, 068.
  176. Reehorst, Marten, Slava Rychkov, David Simmons-Duffin, Benoit Sirois, Ning Su, and Balt van Rees, 2021, “Navigator function for the conformal bootstrap,” SciPost Phys. 11, 072.
  177. Reehorst, Marten, Slava Rychkov, Benoit Sirois, and Balt C. van Rees, 2024, “Bootstrapping frustrated magnets: The fate of the chiral O(N)×O(2) universality class,” arXiv:2405.19411.
  178. Reehorst, Marten, and Benoit Sirois, 2023, “Bootstrapping frustrated magnets: O(N)×O(2) model,” lecture, Bootstrap 2023, Saõ Paulo, 2023, https://www.youtube.com/live/_p1Q4RmTQak?feature=share.
  179. Reehorst, Marten, Emilio Trevisani, and Alessandro Vichi, 2020, “Mixed scalar-current bootstrap in three dimensions,” J. High Energy Phys. 12, 156.
  180. Ribault, Sylvain, 2023, “Diagonal fields in critical loop models,” SciPost Phys. Core 6, 020.
  181. Rong, Junchen, and Slava Rychkov, 2023, “Classifying irreducible fixed points of five scalar fields in perturbation theory,” arXiv:2306.09419.
  182. Rong, Junchen, and Ning Su, 2018, “Scalar CFTs and their large N limits,” J. High Energy Phys. 09, 103.
  183. Rong, Junchen, and Ning Su, 2021a, “Bootstrapping the N=1 Wess-Zumino models in three dimensions,” J. High Energy Phys. 06, 153.
  184. Rong, Junchen, and Ning Su, 2021b, “Bootstrapping the minimal N=1 superconformal field theory in three dimensions,” J. High Energy Phys. 06, 154.
  185. Rong, Junchen, and Ning Su, 2023, “From O(3) to cubic CFT: Conformal perturbation and the large charge sector,” arXiv:2311.00933.
  186. Rong, Junchen, and Jierong Zhu, 2020, “On the ϕ3 theory above six dimensions,” J. High Energy Phys. 04, 151.
  187. Rychkov, Slava, 2020, “Open problems in conformal bootstrap. Problem 1: Bootstrap proof of first-order transitions?,” https://sites.google.com/site/slavarychkov/open-problems-in-conformal-bootstrap.
  188. Sachdev, Subir, 2011, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, England).
  189. Senthil, T., Leon Balents, Subir Sachdev, Ashvin Vishwanath, and Matthew P. A. Fisher, 2004, “Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm,” Phys. Rev. B 70, 144407.
  190. Senthil, T., Ashvin Vishwanath, Leon Balents, Subir Sachdev, and Matthew P. A. Fisher, 2004, “Deconfined quantum critical points,” Science 303, 1490–1494.
  191. Simmons-Duffin, David, 2015, “A semidefinite program solver for the conformal bootstrap,” J. High Energy Phys. 06, 174.
  192. Simmons-Duffin, David, 2016, computer code hyperion, https://github.com/davidsd/hyperion.
  193. Simmons-Duffin, David, 2017, “The lightcone bootstrap and the spectrum of the 3d Ising CFT,” J. High Energy Phys. 03, 086.
  194. Sirois, Benoit, 2022, “Navigating through the O(N) archipelago,” SciPost Phys. 13, 081.
  195. Song, Xue-Yang, Yin-Chen He, Ashvin Vishwanath, and Chong Wang, 2020, “From Spinon Band Topology to the Symmetry Quantum Numbers of Monopoles in Dirac Spin Liquids,” Phys. Rev. X 10, 011033.
  196. Song, Xue-Yang, Chong Wang, Ashvin Vishwanath, and Yin-Chen He, 2019, “Unifying description of competing orders in two dimensional quantum magnets,” Nat. Commun. 10, 4254.
  197. Stergiou, Andreas, 2019, “Bootstrapping MN and tetragonal CFTs in three dimensions,” SciPost Phys. 7, 010.
  198. Stergiou, Andreas, 2018, “Bootstrapping hypercubic and hypertetrahedral theories in three dimensions,” J. High Energy Phys. 05, 035.
  199. Su, Ning, 2019, computer code simpleboot, https://gitlab.com/bootstrapcollaboration/simpleboot.
  200. Su, Ning, 2020, letter to Slava Rychkov (March 7, 2020).
  201. Su, Ning, 2022a, “Skydiving to bootstrap islands: An algorithm for dynamically constrained SDP,” lecture, 2022 Simons Collaboration on the Nonperturbative Bootstrap Annual Meeting, 2022, https://www.simonsfoundation.org/event/simons-collaboration-on-the-nonperturbative-bootstrap-annual-meeting-2022/.
  202. Su, Ning, 2022b, “The hybrid bootstrap,” arXiv:2202.07607.
  203. Su, Ning, 2023, “Semidefinite program and the navigator function,” lecture, Mini-Course of Numerical Conformal Bootstrap, 2023, https://pirsa.org/23040145.
  204. Takahashi, Jun, Hui Shao, Bowen Zhao, Wenan Guo, and Anders W. Sandvik, 2024, “SO(5) multicriticality in two-dimensional quantum magnets,” arXiv:2405.06607.
  205. Wikipedia, 2024a, “Delaunay triangulation,” https://en.wikipedia.org/wiki/Delaunay_triangulation.
  206. Wikipedia, 2024b, “Broyden-Fletcher-Goldfarb-Shanno algorithm,” https://en.wikipedia.org/wiki/Broyden-Fletcher-Goldfarb-Shanno_algorithm.
  207. Wilson, Kenneth G., 1969, “Non-Lagrangian models of current algebra,” Phys. Rev. 179, 1499–1512.
  208. Xu, Cenke, and Yi-Zhuang You, 2015, “Self-dual quantum electrodynamics as boundary state of the three-dimensional bosonic topological insulator,” Phys. Rev. B 92, 220416.
  209. Zerf, Nikolai, Luminita N. Mihaila, Peter Marquard, Igor F. Herbut, and Michael M. Scherer, 2017, “Four-loop critical exponents for the Gross-Neveu-Yukawa models,” Phys. Rev. D 96, 096010.
  210. Zhou, Zheng, Liangdong Hu, W. Zhu, and Yin-Chen He, 2024, “SO(5) Deconfined Phase Transition under the Fuzzy-Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum,” Phys. Rev. X 14, 021044.
  211. Zhu, Wei, Chao Han, Emilie Huffman, Johannes S. Hofmann, and Yin-Chen He, 2023, “Uncovering Conformal Symmetry in the 3D Ising Transition: State-Operator Correspondence from a Quantum Fuzzy Sphere Regularization,” Phys. Rev. X 13, 021009.

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Rev. Mod. Phys. 96, 045004– Published 21 November, 2024
  • Received 1 March 2024
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