Exact Kähler potential from gauge theory and mirror symmetry

By Joaquim Gomis, Sungjay Lee. 2012

214 citations recorded by the source corpus.

A bstractWe prove a recent conjecture that the partition function of $ \mathcal{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 $ \mathcal{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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1af0a3f9dc3e62fd23b861f930716e0c80ad0b73

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Citations in the corpus

Supersymmetry on curved spaces and holography (2012, background): “Subsequently it was conjectured in [32] that, when the CFT2 is related to a GLSM with Calabi-Yau target space X3, the localised path integral computes exactly the quantum Kähler moduli space of X3, see [33] for a proof that this indeed is true.”
Correlation functions of Coulomb branch operators (2016, background): “For SCFTs with one exactly marginal coupling and a one-dimensional Coulomb branch, namely for N = 2 SU(2) SQCD with four fundamental hypermultiplets Extending the earlier result in two-dimensional N = (2, 2) SCFTs [5, 7–9].”
Supersymmetric field theories on three-manifolds (2012, background): “1 For related work in two and five dimensions, see [14-16] and [17-20], respectively.”
A topologically twisted index for three-dimensional supersymmetric theories (2015, methodology): “The partition function on the sphere with no twist have also been computed via localization in [18, 19] and has led to a re-interpretation of the Kähler geometry of the Calabi-Yau moduli space [60, 61].”
Sphere partition functions and the Zamolodchikov metric (2014, methodology): “5) by generalizing the argument of [15] (i.”
Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary (2013, background): “Although there is some attempt [21], the real understanding of the realtion between ZS2 and RR〈0|0〉RR is still missing.”