Mathematics

We propose the functional equations for the partition function of 6d SCFT, which can be regarded as the elltipic version of Nakajima-Yoshioka's K-theoretic blowup equations. We find the blowup equations combined together are sufficient to determine the partition function completely. In particular, we derive the recursion formula for the elliptic genus of 6d SCFT from blowup equations. As examples, we study 6d $(1,0)$ minimal SCFT with gauge group $SU(3)$ and $SO(8)$ and also E-strings. This is based on a to appear paper joint with Jie Gu, Babak Haghighat and Xin Wang.