- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Making supersymmetric connected N=(0,2) sigma models

Mikhail Shifman1,2,3, Arkady Vainshtein1,2,4, and Alexei Yung2,5

  • 1Department of Physics, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 3Institut des Hautes Études Scientifiques, 35 Route de Chartres, 91440 Bures-sur-Yvette, France
  • 4Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
  • 5Petersburg Nuclear Physics Institute, Gatchina, Leningrad District 188300, Russia

PDF

Phys. Rev. D 91, 045010 – Published 9 February, 2015

DOI: https://doi.org/10.1103/PhysRevD.91.045010

Abstract

We construct “connected” (0, 2) sigma models starting from n copies of (2, 2) CP(N−1) models. General aspects of models of this type (known as T+O deformations) had been previously studied in the context of heterotic string theories. Our construction presents a natural generalization of the nonminimally deformed (2, 2) model with an extra (0, 2) fermion superfield on tangent bundle T[CP(N−1)×C1]. We had thoroughly analyzed the latter model previously and found the exact β function and a spontaneous breaking of supersymmetry. In contrast, in certain connected sigma models the spontaneous breaking of supersymmetry disappears. We study the connected sigma models in the large-N limit finding supersymmetric vacua and determining the particle spectrum. While the Witten index vanishes in all the models under consideration, in these special cases of connected models, one can use a permutation symmetry to define a modification of the Witten index which does not vanish. This eliminates the spontaneous breaking of supersymmetry. We then examine the exact β functions of our connected (0, 2) sigma models.

View figure in article

Article Text

References (26)

  1. A. M. Polyakov, Interaction of Goldstone particles in two dimensions. Applications to ferromagnets and massive Yang-Mills fields, Phys. Lett. 59B, 79 (1975).
  2. E. Witten, New issues in manifolds of SU(3) holonomy, Nucl. Phys. B268, 79 (1986); M. Dine and N. Seiberg, Are (0, 2) models string miracles?, B306, 137 (1988).
  3. J. Distler and S. Kachru, (0, 2) Landau-Ginzburg theory, Nucl. Phys. B413, 213 (1994); M. Bertolini, I. V. Melnikov, and M. R. Plesser, Accidents in (0, 2) Landau-Ginzburg theories, J. High Energy Phys. 12 (2014) 157.
  4. A. Gadde, S. Gukov, and P. Putrov, (0, 2) trialities, J. High Energy Phys. 03 (2014) 076.
  5. A. Gadde, S. Gukov, and P. Putrov, Exact solutions of 2d supersymmetric gauge theories, arXiv:1404.5314.
  6. M. Edalati and D. Tong, Heterotic vortex strings, J. High Energy Phys. 05 (2007) 005.
  7. M. Shifman and A. Yung, Heterotic flux tubes in N=2 SQCD with N=1 preserving deformations, Phys. Rev. D 77, 125016 (2008); 79, 049901(E) (2009).
  8. A. Hanany and D. Tong, Vortices, instantons and branes, J. High Energy Phys. 07 (2003) 037; R. Auzzi, S. Bolognesi, J. Evslin, K. Konishi, and A. Yung, Non-Abelian superconductors: Vortices and confinement in N=2 SQCD, Nucl. Phys. B673, 187 (2003); M. Shifman and A. Yung, Non-Abelian string junctions as confined monopoles, Phys. Rev. D 70, 045004 (2004); A. Hanany and D. Tong, Vortex strings and four-dimensional gauge dynamics, J. High Energy Phys. 04 (2004) 066.
  9. B. Zumino, Supersymmetry, and Kähler manifolds, Phys. Lett. 87B, 203 (1979).
  10. M. Shifman and A. Yung, Large-N solution of the heterotic N=(0,2) two-dimensional CP(N−1) model, Phys. Rev. D 77, 125017 (2008); 81, 089906(E) (2010).
  11. P. West, Introduction to Supersymmetry and Supergravity, 2nd ed. (World Scientific, Singapore, 1990), Chap. 23.
  12. E. Witten, Two-dimensional models with (0, 2) supersymmetry: Perturbative aspects, Adv. Theor. Math. Phys. 11, 1 (2007).
  13. M.-C. Tan and J. Yagi, Chiral algebras of (0, 2) sigma models: Beyond perturbation theory, Lett. Math. Phys. 84, 257 (2008).
  14. J. Yagi, Chiral algebras of (0, 2) models, Adv. Theor. Math. Phys. 16, 1 (2012).
  15. B. Jia, E. Sharpe, and R. Wu, Notes on non-Abelian (0, 2) theories and dualities, J. High Energy Phys. 08 (2014) 017.
  16. T. T. Dumitrescu and N. Seiberg, Supercurrents and brane currents in diverse dimensions, J. High Energy Phys. 07 (2011) 095.
  17. M. Shifman and A. Yung, Two-dimensional sigma models related to non-Abelian strings in super-Yang-Mills, arXiv:1401.7067.
  18. E. Witten, Elliptic genera and quantum field theory, Commun. Math. Phys. 109, 525 (1987).
  19. E. Witten, Constraints on supersymmetry breaking, Nucl. Phys. B202, 253 (1982).
  20. E. Witten, Instantons, The quark model, and the 1/n expansion, Nucl. Phys. B149, 285 (1979).
  21. E. Witten, Phases of N=2 theories in two dimensions, Nucl. Phys. B403, 159 (1993).
  22. J. Chen, X. Cui, M. Shifman, and A. Vainshtein, N=(0,2) deformation of (2, 2) sigma models: Geometric structure, holomorphic anomaly and exact beta functions, Phys. Rev. D 90, 045014 (2014).
  23. A. Gorsky, M. Shifman, and A. Yung, Non-Abelian Meissner effect in Yang-Mills theories at weak coupling, Phys. Rev. D 71, 045010 (2005).
  24. P. Bolokhov, M. Shifman, and A. Yung (to be published).
  25. F. Benini, R. Eager, K. Hori, and Y. Tachikawa, Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups, Lett. Math. Phys. 104, 465 (2014); Elliptic genera of 2d N=2 gauge theories, arXiv:1308.4896.
  26. X. Cui and M. Shifman, Perturbative aspects of heterotically deformed CP(N−1) sigma model, Phys. Rev. D 82, 105022 (2010).

Outline

Information

Phys. Rev. D 91, 045010– Published 9 February, 2015
  • Received 15 July 2014
Article part of CHORUS

© 2015 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation