Gukov–Pei–Putrov–Vafa conjecture for \(SU(N)/{\mathbb {Z}}_m\)

Abstract

In our earlier work, we studied the \({\hat{Z}}\)-invariant(or homological blocks) for SO(3) gauge group and we found it to be same as \({\hat{Z}}^{SU(2)}\). This motivated us to study the \({\hat{Z}}\)-invariant for quotient groups \(SU(N)/{\mathbb {Z}}_m\), where m is some divisor of N. Interestingly, we find that \({\hat{Z}}\)-invariant is independent of m.