Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

A relation between circular 1/2 BPS ’t Hooft operators in 4d \({{\mathcal N}=4}\) SYM and instantonic solutions in 2D Yang-Mills theory (YM2) has recently been conjectured. Localization indeed predicts that those ’t Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM2, belonging to representations of the dual group L G. This conjecture has been tested in the case G = U(N) =  L G and for fundamental representations. In this paper, we examine this conjecture for the case of the groups G = SU(N) and L G = SU(N)/Z N and loops in different representations. Peculiarities when groups are not self-dual and representations not “minimal” are pointed out.