Gauge Theory Dynamics and Calabi-Yau Moduli
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We compute the exact partition function of two dimensional N=(2,2) supersymmetric gauge theories on S². For theories with SU(2|1)_A invariance, the partition function admits two equivalent representations corresponding to localization on the Coulomb branch or the Higgs branch, which includes vortex and anti-vortex excitations at the poles. For SU(2|1)_B invariant gauge theories, the partition function is localized to the Higgs branch which is generically a Kähler quotient manifold. The resulting partition functions are invariant under the renormalization group flow. For gauge theories that flow in the infrared to Calabi-Yau nonlinear sigma models, the partition functions for the SU(2|1)_A (resp SU(2|1)_B) invariant theories compute the Kähler potential on the Kähler moduli (resp. complex structure moduli) of the Calabi-Yau manifold. We also compute the elliptic genus of such theories in the presence of Stückelberg fields and show that they are modular completions of mock Jacobi forms.
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Nima Doroud (2014). Gauge Theory Dynamics and Calabi-Yau Moduli. UWSpace. http://hdl.handle.net/10012/8557