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$tt^*$ Toda equations for surface defects in ${\mathcal N}=2$ SYM and instanton counting for classical Lie groups
The partition function of $\mathcal{N}=2$ super Yang-Mills theories with arbitrary simple gauge group coupled to a self-dual $\Omega$-background is shown to be fully determined by studying the renormalization group equations relevant to the surface operators generating its one-form symmetries. The corresponding system of equations results in a ${\it non-autonomous}$ Toda …