Monopoles and instantons on partially compactified <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math></span>-branes

Kimyeong Lee; Piljin Yi

doi:10.1103/PhysRevD.56.3711

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Monopoles and instantons on partially compactified $D$ -branes

Kimyeong Lee and Piljin Yi

Physics Department, Columbia University, New York, New York 10027

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Phys. Rev. D 56, 3711 – Published 15 September, 1997

DOI: https://doi.org/10.1103/PhysRevD.56.3711

Abstract

Motivated by the recent $D$ -brane constructions of world-volume monopoles and instantons, we study the supersymmetric SU $(N)$ Yang-Mills theory on $S^{1} \times R^{3 + 1}$ , spontaneously broken by a Wilson loop. In addition to the usual $N - 1$ fundamental monopoles, the $N$ th Bogomol'nyi-Prasad-Sommerfield monopole appears from the Kaluza-Klein sector. When all $N$ monopoles are present, net magnetic charge vanishes and the solution can be reinterpreted as a Wilson-loop instanton of unit Pontryagin number. The instanton-multimonopole moduli space is explicitly constructed, and seen to be identical to a Coulomb phase moduli space of a U ${(1)}^{N}$ gauge theory in $2 + 1$ dimensions related to Kronheimer's gauge theory of SU $(N)$ -type. This extends the results by Intriligator and Seiberg to the finite couplings that, in the infrared limit of Kronheimer's theory, the Coulomb phase parametrizes a centered SU $(N)$ instanton. We also elaborate on the case of restored SU $(N)$ symmetry.

References (25)

J. Polchinski, “TASI lectures on $D$ -branes,” hep-th/9611050, and references therein.
E. Witten, Nucl. Phys. B460, 335 (1996).
J. Polchinski, Phys. Rev. Lett. 75, 4724 (1995).
A. Strominger, Phys. Lett. B 383, 44 (1996); M. B. Green and M. Gutperle, 377, 28 (1996); A. A. Tseytlin, Nucl. Phys. B469, 51 (1996).
D.-E. Diaconescu, “ $D$ -branes, monopoles and Nahm equations,” hep-th/9608163; M. R. Douglas and M. Li, “D-brane realization of $N = 2$ super Yang-Mills theory in four dimensions,” hep-th/9604041.
M. R. Douglas, “Gauge fields and $D$ -branes,” hep-th/9604198; E. Witten, Nucl. Phys. B460, 541 (1996); M. R. Douglas and G. Moore, “ $D$ -branes, quivers, and ALE instantons,” hep-th/9603167.
E. B. Bogomol'nyi, Sov. J. Nucl. Phys. 24, 449 (1976); M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975); S. Coleman, S. Parke, A. Neveu and C. M. Sommerfield, Phys. Rev. D 15, 544 (1977).
E. J. Weinberg, Nucl. Phys. B203, 445 (1982).
S. Katz and C. Vafa, “Geometric engineering of $N = 1$ quantum field theories,” hep-th/9611090.
L. S. Brown, R. D. Carlitz, and C. Lee, Phys. Rev. D 16, 417 (1977).
G. W. Gibbons and N. S. Manton, Phys. Lett. B 356, 32 (1995).
K. Lee, E. J. Weinberg, and P. Yi, Phys. Rev. D 54, 1633 (1996).
M. K. Murray, “A note on the (1,1,…,1) monopole metric,” hep-th/9605054; G. Chalmers, “Multimonopole moduli spaces for SU $(N)$ gauge group,” hep-th/9605182.
K. Intriligator and N. Seiberg, Phys. Lett. B 387, 513 (1996).
A. Hanany and E. Witten, Nucl. Phys. B492, 152 (1997).
P. B. Kronheimer, J. Diff. Geom. 29, 665 (1989).
J. de Boer, H. Kori, H. Ooguri, and Y. Oz, Nucl. Phys. B493, 148 (1997); M. Porrati and A. Zaffaroni, B490, 107 (1997).
G. W. Gibbons and P. Rychenkova, “Hyper-Kähler quotient construction of BPS monopole moduli spaces,” hep-th/9608085; A. Dancer and A. Swann, J. Geom. Phys. (to be published); E. Calabi, in The Chern Symposium, 1979, edited by W.-Y. Hsiang et al. (Springer-Verlag, New York, 1980).
K. Lee, E. J. Weinberg, and P. Yi, Phys. Lett. B 376, 97 (1996); J. P. Gauntlett and D. A. Lowe, Nucl. Phys. B472, 194 (1996); S. A. Connell (unpublished).
P. Rossi, Nucl. Phys. B149, 170 (1979); B. J. Harrington and H. K. Shepard, Phys. Rev. D 17, 2122 (1978); D. Gross, R. Pisarksi and L. G. Yaffe, Rev. Mod. Phys. 53, 43 (1981).
K. Lee, E. J. Weinberg and P. Yi, Phys. Rev. D 54, 6351 (1996).
G. W. Gibbons, Phys. Lett. B 382, 53 (1996).
W. Nahm, Phys. Lett. 90B, 413 (1980).
W. Nahm, in Group Theoretical Methods in Physics, edited by G. Denardo (Springer-Verlag, Berlin, 1984).
H. Garland and M. Murray, Commun. Math. Phys. 120, 335 (1988).

[c1] J. Polchinski, “TASI lectures on $D$ -branes,” hep-th/9611050, and references therein.

[c2] E. Witten, Nucl. Phys. B460, 335 (1996).

[c3] J. Polchinski, Phys. Rev. Lett. 75, 4724 (1995).

[c4] A. Strominger, Phys. Lett. B 383, 44 (1996); M. B. Green and M. Gutperle, 377, 28 (1996); A. A. Tseytlin, Nucl. Phys. B469, 51 (1996).

[c5] D.-E. Diaconescu, “ $D$ -branes, monopoles and Nahm equations,” hep-th/9608163; M. R. Douglas and M. Li, “D-brane realization of $N = 2$ super Yang-Mills theory in four dimensions,” hep-th/9604041.

[c6] M. R. Douglas, “Gauge fields and $D$ -branes,” hep-th/9604198; E. Witten, Nucl. Phys. B460, 541 (1996); M. R. Douglas and G. Moore, “ $D$ -branes, quivers, and ALE instantons,” hep-th/9603167.

[c7] E. B. Bogomol'nyi, Sov. J. Nucl. Phys. 24, 449 (1976); M. K. Prasad and C. M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975); S. Coleman, S. Parke, A. Neveu and C. M. Sommerfield, Phys. Rev. D 15, 544 (1977).

[c8] E. J. Weinberg, Nucl. Phys. B203, 445 (1982).

[c9] S. Katz and C. Vafa, “Geometric engineering of $N = 1$ quantum field theories,” hep-th/9611090.

[c10] L. S. Brown, R. D. Carlitz, and C. Lee, Phys. Rev. D 16, 417 (1977).

[c11] G. W. Gibbons and N. S. Manton, Phys. Lett. B 356, 32 (1995).

[c12] K. Lee, E. J. Weinberg, and P. Yi, Phys. Rev. D 54, 1633 (1996).

[c13] M. K. Murray, “A note on the (1,1,…,1) monopole metric,” hep-th/9605054; G. Chalmers, “Multimonopole moduli spaces for SU $(N)$ gauge group,” hep-th/9605182.

[c14] K. Intriligator and N. Seiberg, Phys. Lett. B 387, 513 (1996).

[c15] A. Hanany and E. Witten, Nucl. Phys. B492, 152 (1997).

[c16] P. B. Kronheimer, J. Diff. Geom. 29, 665 (1989).

[c17] J. de Boer, H. Kori, H. Ooguri, and Y. Oz, Nucl. Phys. B493, 148 (1997); M. Porrati and A. Zaffaroni, B490, 107 (1997).

[c18] G. W. Gibbons and P. Rychenkova, “Hyper-Kähler quotient construction of BPS monopole moduli spaces,” hep-th/9608085; A. Dancer and A. Swann, J. Geom. Phys. (to be published); E. Calabi, in The Chern Symposium, 1979, edited by W.-Y. Hsiang et al. (Springer-Verlag, New York, 1980).

[c19] K. Lee, E. J. Weinberg, and P. Yi, Phys. Lett. B 376, 97 (1996); J. P. Gauntlett and D. A. Lowe, Nucl. Phys. B472, 194 (1996); S. A. Connell (unpublished).

[c20] P. Rossi, Nucl. Phys. B149, 170 (1979); B. J. Harrington and H. K. Shepard, Phys. Rev. D 17, 2122 (1978); D. Gross, R. Pisarksi and L. G. Yaffe, Rev. Mod. Phys. 53, 43 (1981).

[c21] K. Lee, E. J. Weinberg and P. Yi, Phys. Rev. D 54, 6351 (1996).

[c22] G. W. Gibbons, Phys. Lett. B 382, 53 (1996).

[c23] W. Nahm, Phys. Lett. 90B, 413 (1980).

[c24] W. Nahm, in Group Theoretical Methods in Physics, edited by G. Denardo (Springer-Verlag, Berlin, 1984).

[c25] H. Garland and M. Murray, Commun. Math. Phys. 120, 335 (1988).

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Monopoles and instantons on partially compactified D-branes

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Monopoles and instantons on partially compactified $D$ -branes