Exact Kähler potential from gauge theory and mirror symmetry

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 Kähler potential on the quantum Kähler 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 su-

Ellipsoid partition function from Seiberg-Witten monopoles

“…Indeed, recently a lot of research has been conducted on interpreting and applying the wide variety of exact results available, resulting in an impressive list of both physical and mathematical developments. To name a few, the N = (2, 2) S 2 partition function [5,6] computes the exact Kähler potential on the quantum Kähler moduli space of Calabi-Yau manifolds [34][35][36], the N = 2 S 3 partition function [11][12][13][14] is essential in the F-theorem [37], and the partition function of four-dimensional N = 2 theories placed on an ellipsoid [1,22] equals, for theories of class S, a Liouville/Toda correlator [38,39], while for superconformal theories it also computes the Kähler potential on the superconformal manifold [36,40]. Localization computations are based on the observation that in the path integral of a supersymmetric theory one can add Q-exact 2 deformations to the action without changing the resulting partition function.…”

The stringy instanton partition function

“…We will show in this section that these corrections compute the Gromov-Witten invariants and gravitational descendants of the ADHM moduli space. It has been argued in [18] and shown in [19] that the spherical partition function computes the vacuum amplitude of the non-linear σ-model (NLSM) in the infrared…”

Localization of supersymmetric Chern-Simons-Matter theory on a squashed S 3 with SU(2) × U(1) isometry

“…In recent years, it has revived due to the work of Pestun [4] and Kapustin, Willett, Yaakov [5]. Inspired by these works, supersymmetric theories on curved spacetimes are being studied intensively [6][7][8][9][10][11][12][13][14][15][16].…”