Class S theories on S Satoshi Nawata, Yiwen Pan, Jiahao Zheng

We study two-dimensional N=(0,2) and N=(0,4) theories derived from compactifying class S theories on S2 with a topological twist. We present concise expressions for the elliptic genera of both classes of theories, revealing the topological quantum field theory structure on Riemann surfaces Cg,n. Furthermore, our study highlights the relationship between the left-moving sector of the (0,2) theory and the chiral algebra of the four-dimensional N=2 theory. Notably, we propose that the (0,2) elliptic genus of a theory of this class can be expressed as a linear combination of characters of the corresponding chiral algebra.