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

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