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We calculate the instanton partition function of the four-dimensional \( \mathcal{N}={2}^{\star } \) SU(N) gauge theory in the presence of a generic surface operator, using equivariant localization. By analyzing the constraints that arise from S-duality, we show that the effective twisted superpotential, which governs the infrared dynamics of the two-dimensional theory on the ...

We study \( \mathcal{N} \) = 2⋆ theories with gauge group U(N ) and use equivariant localization to calculate the quantum expectation values of the simplest chiral ring elements. These are expressed as an expansion in the mass of the adjoint hypermultiplet, with coefficients given by quasi-modular forms of the S-duality group. Under the action of this group, we construct ...

We use localization techniques to study the non-perturbative properties of an \( \mathcal{N}=2 \) superconformal gauge theory with gauge group SU(3) and six fundamental flavours. The instanton corrections to the prepotential, the dual periods and the period matrix are calculated in a locus of special vacua possessing a ℤ 3 symmetry. In a semiclassical expansion, we show that these ...

We consider the local F-theory set-up corresponding to four D7 branes in type I′ theory, in which the exact axio-dilaton background τ(z) is identified with the low-energy effective coupling of the four-dimensional \( \mathcal{N} = 2 \) super Yang-Mills theory with gauge group SU(2) and N f = 4 flavours living on a probe D3 brane placed at position z. Recently, an intriguing ...