Supersymmetric index on T^2 x S^2 and elliptic genus

Abstract

We study partition function of four-dimensional $\mathcal{N}=1$ supersymmetric field theory on $T^2\times S^2$. By applying supersymmetry localization, we show that the $T^2\times S^2$ partition function is given by elliptic genus of certain two-dimensional $\mathcal{N}=(0,2)$ theory. As an application, we discuss a relation between 4d Seiberg duality duality and 2d $(0,2)$ triality, proposed by Gadde, Gukov and Putrov. In other examples, we identify 4d theories giving elliptic genera of K3, M-strings and E-strings. In the example of K3, we find that there are two 4d theories giving the elliptic genus of K3. This would imply new four-dimensional duality.

arXiv comment38+12 pages

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Cited by in corpus (13)

• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• New 2d $\mathcal{N}=(0,2)$ dualities from four dimensions
• A 2d (0,2) appetizer
• Integrability from 2d N=(2,2) Dualities
• Supersymmetric solutions and Borel singularities for N=2 supersymmetric Chern-Simons theories
• Supersymmetric indices on $I\times T^2$, elliptic genera and dualities with boundaries
• Factorising the 3D Topologically Twisted Index
• Lectures on 4d N=1 dynamics and related topics
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• N=2 minimal model from 4d supersymmetric theory