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Three Dimensional Mirror Symmetry and Partition Function on $S^3$ · Around

2013

Three Dimensional Mirror Symmetry and Partition Function on $S^3$

Dey, Anindya, Distler, Jacques

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We provide non-trivial checks of $\mathcal{N}=4, D=3$ mirror symmetry in a large class of quiver gauge theories whose Type IIB (Hanany-Witten) descriptions involve D3 branes ending on orbifold/orientifold 5-planes at the boundary.

From the M-theory perspective, such theories can be understood in terms of coincident M2 branes sitting at the origin of a product of an A-type and a D-type ALE (Asymtotically Locally Euclidean) space with G-fluxes.
Families of mirror dual pairs, which arise in this fashion, can be labeled as $(A_{m-1},D_n)$, where $m$ and $n$ are integers.
For a large subset of such infinite families of dual theories, corresponding to generic values of $n\geq 4$, arbitrary ranks of the gauge groups and varying $m$, we test the conjectured duality by proving the precise equality of the $S^3$ partition functions for dual gauge theories in the IR as functions of masses and FI parameters.

Built on

K. A. Intriligator and N. Seiberg, “Mirror symmetry in three-dimensional gauge theories,” Phys.Lett
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J. de Boer, K. Hori, H. Ooguri, and Y. Oz, “Mirror symmetry in three-dimensional gauge theories, quivers and D-branes,” Nucl.Phys
1997
Earlier work this paper cites.
M. Porrati and A. Zaffaroni, “M theory origin of mirror symmetry in three-dimensional gauge theories,” Nucl.Phys
1997
Earlier work this paper cites.
A. Hanany and E. Witten, “Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics,” Nucl.Phys
1997
Earlier work this paper cites.

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A. Kapustin, B. Willett, and I. Yaakov, “Tests of Seiberg-like duality in three dimensions,” arXiv:1012.4021 [hep-th]
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Then

A. Kapustin, B. Willett, and I. Yaakov, “Exact results for Wilson loops in superconformal Chern-Simons theories with matter,” JHEP
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2010
Later among the works it cites.
A. Kapustin, B. Willett, and I. Yaakov, “Nonperturbative tests of three-dimensional dualities,” JHEP
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2010
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G. Festuccia and N. Seiberg, “Rigid supersymmetric theories in curved superspace,” JHEP
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2011
Later among the works it cites.
A. Dey, “On three-dimensional mirror symmetry,” JHEP
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2012
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