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arXiv · 1312.2361

Connecting Mirror Symmetry in 3d and 2d via Localization

Heng-Yu Chen·Hsiao-Yi Chen·Jun-Kai Ho
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Abstract

We explicitly apply localization results to study the interpolation between three and two dimensional mirror symmetry for Abelian gauge theories with four supercharges. We first use the ellipsoid S_b^3 partition functions to verify the mirror symmetry between a pair of general three dimensional N=2 Abelian Chern-Simons quiver gauge theories. These expressions readily factorize into holomorphic blocks and their anti-holomorphic copies, so we can also obtain the partition functions on S^1 x S^2 via fusion procedure. We then demonstrate S^1 x S^2 partition functions for the three dimensional Abelian gauge theories can be dimensionally reduced to the S^2 partition functions of N=(2,2) GLSM and Landau-Ginzburg model for the corresponding two dimensional mirror pair, as anticipated previously in \cite{Aganagic:2001uw}. We also comment on the analogous interpolation for the non-Abelian gauge theories and compute the K-theory vortex partition function for a simple limit to verify the prediction from holomorphic block.

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Heng-Yu Chen, Hsiao-Yi Chen, Jun-Kai Ho. 2013-12-09. Connecting Mirror Symmetry in 3d and 2d via Localization. https://doi.org/10.1142/s0217751x15300045

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