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Exact Kähler potential from gauge theory and mirror symmetry

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Abstract

We 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.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Jaume Gomis

  2. DAMTP, Centre for Mathematical Sciences, Cambridge University, Cambridge, CB3 0WA, U.K

    Sungjay Lee

Authors
  1. Jaume Gomis
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  2. Sungjay Lee
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Correspondence to Sungjay Lee.

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ArXiv ePrint: 1210.6022

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Gomis, J., Lee, S. Exact Kähler potential from gauge theory and mirror symmetry. J. High Energ. Phys. 2013, 19 (2013). https://doi.org/10.1007/JHEP04(2013)019

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