Solution of \(N=2\) gauge theories via compactification to three dimensions.(English)Zbl 1079.81571
Summary: A number of \(N=2\) gauge theories can be realized by brane configurations in type IIA string theory. One way of solving them involves lifting the brane configuration to M-theory. In this paper we present an alternative way of analyzing a subclass of these theories (elliptic models). We observe that upon compactification on a circle one can use a version of mirror symmetry to map the original brane configuration into one containing only D-branes. Simultaneously the Coulomb branch of the four-dimensional theory is mapped to the Higgs branch of a five-dimensional theory with three-dimensional impurities. The latter does not receive quantum corrections and can be analyzed exactly. The solution is naturally formulated in terms of an integrable system, which is a version of a Hitchin system on a punctured torus.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
Cite
References:
| [1] | Witten, E., Solutions of four-dimensional field theories via M-Theory, Nucl. Phys. B, 500, 3 (1997) ·Zbl 0934.81066 |
| [2] | Gorskii, A., Integrability and Seiberg-Witten exact solution, Phys. Lett. B, 355, 466 (1995) ·Zbl 0997.81567 |
| [3] | Martinec, E.; Warner, N., Integrable systems and supersymmetric gauge theory, Nucl. Phys. B, 459, 97 (1996) ·Zbl 0996.37506 |
| [4] | Donagi, R.; Witten, E., Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B, 460, 299 (1996) ·Zbl 0996.37507 |
| [5] | Hitchin, N., Stable bundles and integrable systems, Duke Math. J., 54, 91 (1987) ·Zbl 0627.14024 |
| [6] | A. Gorsky, S. Gukov and A. Mironov, Multiscale \(N\); A. Gorsky, S. Gukov and A. Mironov, Multiscale \(N\) |
| [7] | R. Donagi, L. Ein and R. Lazarsfeld, A non-linear deformation of the Hitchin dynamical system, alg-geom/9504017.; R. Donagi, L. Ein and R. Lazarsfeld, A non-linear deformation of the Hitchin dynamical system, alg-geom/9504017. ·Zbl 0824.14013 |
| [8] | S. Gukov, Seiberg-Witten solution from Matrix theory, hep-th/9709138.; S. Gukov, Seiberg-Witten solution from Matrix theory, hep-th/9709138. |
| [9] | Intriligator, K.; Seiberg, N., Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B, 387, 513 (1996) ·Zbl 0991.81588 |
| [10] | Seiberg, N.; Witten, E., Monopoles, duality, and chiral symmetry breaking in \(N = 2\) supersymmetric QCD, Nucl. Phys. B, 431, 484 (1994) ·Zbl 1020.81911 |
| [11] | de Boer, J., Mirror symmetry in three-dimensional gauge theories, quivers, and D-branes, Nucl. Phys. B, 493, 101 (1997) ·Zbl 0973.14507 |
| [12] | Hanany, A.; Witten, E., Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B, 492, 152 (1997) ·Zbl 0996.58509 |
| [13] | A. Kapustin and S. Sethi, The Higgs branch of impurity theories, hep-th/9804027.; A. Kapustin and S. Sethi, The Higgs branch of impurity theories, hep-th/9804027. ·Zbl 0967.81050 |
| [14] | Hitchin, N. J.; Karlhede, A.; Lindström, U.; Roček, M., HyperKähler metrics and supersymmetry, Comm. Math. Phys., 108, 535 (1987) ·Zbl 0612.53043 |
| [15] | Ganor, O.; Sethi, S., New perspectives on Yang-Mills theories with sixteen supersymmetries, J. High Energy Phys., 01, 007 (1998) ·Zbl 0958.81167 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
