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.

38+12 pages

References in corpus (6)

• Localization on Hopf surfaces
• Higher spin AdS_3 holography with extended supersymmetry
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• Holomorphic Blocks for 3d Non-abelian Partition Functions
• Factorization of 4d N=1 superconformal index
• Chiral operators in two-dimensional (0,2) theories and a test of triality

Cited by in corpus (3)

• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
• A New Integrable Ising-type Model from 2d $\mathcal{N}$=(2,2) Dualities