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On Three-Dimensional Mirror Symmetry · Around

2011

On Three-Dimensional Mirror Symmetry

Dey, Anindya

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Mirror Symmetry for a large class of three dimensional $\mathcal{N}=4$ supersymmetric gauge theories has a natural explanation in terms of M-theory compactified on a product of $\text{ALE}$ spaces.

A pair of such mirror duals can be described as two different deformations of the eleven-dimensional supergravity background $\mathcal{M}=\mathbb{R}^{2,1} \times \text{ALE}_{1} \times \text{ALE}_{2}$, to which they flow in the deep IR.
Using the $A-D-E$ classification of $\text{ALE}$ spaces, we present a neat way to catalogue dual quiver gauge theories that arise in this fashion.
In addition to the well-known examples studied in \cite{Intriligator:1996ex}, \cite{deBoer:1996mp}, this procedure leads to new sets of dual theories.

Built on

K. A. Intriligator and N. Seiberg, “Mirror symmetry in three-dimensional gauge theories,” Phys. Lett. B 387
1996
Earlier work this paper cites.
J. de Boer, K. Hori, H. Ooguri and Y. Oz, “Mirror symmetry in three-dimensional gauge theories, quivers and D-branes,” Nucl. Phys. B 493
1997
Earlier work this paper cites.
A. Hanany and E. Witten, “Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics,” Nucl. Phys. B 492
1997
Earlier work this paper cites.
M. Porrati and A. Zaffaroni, “M theory origin of mirror symmetry in three-dimensional gauge theories,” Nucl. Phys. B 490
1997
Earlier work this paper cites.
A. Sen, “A Note on enhanced gauge symmetries in M and string theory,” JHEP 9709
1997
Earlier work this paper cites.

Similar

A. Kapustin, “D(n) quivers from branes,” JHEP 9812
1998
Cited alongside, same era.
A. Hanany and A. Zaffaroni, “Issues on orientifolds: On the brane construction of gauge theories with SO(2n) global symmetry,” JHEP 9907
1999
Cited alongside, same era.
A. Kapustin and M. J. Strassler, JHEP 9904
1999
Cited alongside, same era.
B. Feng and A. Hanany, “Mirror symmetry by O3 planes,” JHEP 0011
2000
Cited alongside, same era.
D. Gaiotto and E. Witten, “Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory,” arXiv:0804.2902 [hep-th]
Original
Cited in the paper.
D. Gaiotto and E. Witten, “S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory,” arXiv:0807.3720 [hep-th]

Then

E. Witten, “Branes, Instantons, And Taub-NUT Spaces,” JHEP 0906
Original
2009
Later among the works it cites.
A. Kapustin, B. Willett and I. Yaakov, “Nonperturbative Tests of Three-Dimensional Dualities,” JHEP 1010
Original
2010
Later among the works it cites.
A. Kapustin, B. Willett and I. Yaakov, “Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter,” JHEP 1003
Original
2010
Later among the works it cites.
A. Sen, “Stable nonBPS bound states of BPS D-branes,” Conf. Proc. C 100523
2010
Later among the works it cites.

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