2012

Exact Kahler Potential from Gauge Theory and Mirror Symmetry

Gomis, Jaume, Lee, Sungjay

Understand

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.

Built on

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Similar

E. Witten, “Phases of N = 2 theories in two dimensions,” Nucl. Phys
1993
Cited alongside, same era.
P. S. Aspinwall, B. R. Greene, and D. R. Morrison, “Multiple mirror manifolds and topology change in string theory,” Phys.Lett
1993
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1995
Cited alongside, same era.
K. Hori and D. Tong, “Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories,” JHEP
2007
Cited alongside, same era.
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2008
Cited alongside, same era.
K. Hosomichi, S. Lee, and J. Park, “AGT on the S-duality Wall,” JHEP
2010
Cited alongside, same era.
N. Doroud, J. Gomis, B. Le Floch, and S. Lee, “Exact Results in D=2 Supersymmetric Gauge Theories,” 1206.2606
Cited in the paper.
F. Benini and S. Cremonesi, “Partition functions of N = ( 2 , 2 CLOSE N=(2,2 ) gauge theories on S 2 S^{2} and vortices,” 1206.2356
Cited in the paper.
H. Jockers, V. Kumar, J. M. Lapan, D. R. Morrison, and M. Romo, “Two-Sphere Partition Functions and Gromov-Witten Invariants,” 1208.6244
Cited in the paper.
K. Hori and C. Vafa, “Mirror symmetry,” hep-th/0002222
Cited in the paper.
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Cited in the paper.
K. Hori, “Duality in two-dimensional (2,2) supersymmetric non-abelian gauge theories,” arXiv/1104.2853
Cited in the paper.

Then

N. Hama, K. Hosomichi, and S. Lee, “SUSY Gauge Theories on Squashed Three-Spheres,” JHEP
2011
Later among the works it cites.
G. Festuccia and N. Seiberg, “Rigid Supersymmetric Theories in Curved Superspace,” JHEP
2011
Later among the works it cites.
N. Hama, K. Hosomichi, and S. Lee, “Notes on SUSY Gauge Theories on Three-Sphere,” JHEP
2011
Later among the works it cites.
N. Drukker, D. Gaiotto, and J. Gomis, “The Virtue of Defects in 4D Gauge Theories and 2D CFTs,” JHEP
2011
Later among the works it cites.
C. Closset, T. T. Dumitrescu, G. Festuccia, Z. Komargodski, and N. Seiberg, “Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories,” JHEP
2012
Closest in time.
D. L. Jafferis, “The Exact Superconformal R-Symmetry Extremizes Z,” JHEP
2012
Closest in time.

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