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arXiv · 1210.6022

Exact Kahler Potential from Gauge Theory and Mirror Symmetry

Jaume Gomis·Sungjay Lee
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Abstract

We prove a recent conjecture that the partition function of N=(2, 2) gauge theories on the two-sphere which flow to Calabi-Yau sigma models in the infrared computes the exact Kahler potential on the quantum Kahler moduli space of the corresponding Calabi-Yau. This establishes the two-sphere partition function as a new method of computation of worldsheet instantons and Gromov-Witten invariants. We also calculate the exact two-sphere partition function for N=(2,2) Landau-Ginzburg models with an arbitrary twisted superpotential W. These results are used to demonstrate that arbitrary abelian gauge theories and their associated mirror Landau-Ginzburg models have identical two-sphere partition functions. We further show that the partition function of non-abelian gauge theories can be rewritten as the partition function of mirror Landau-Ginzburg models.

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Jaume Gomis, Sungjay Lee. 2012-11-20. Exact Kahler Potential from Gauge Theory and Mirror Symmetry. https://doi.org/10.1007/jhep04(2013)019

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