Class S theories on S 2

We study two-dimensional N = ( 0 , 2 ) and N = ( 0 , 4 ) theories derived from compactifying class S theories on S 2 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 C g , 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.