Abstract
Abstract The path integral of a general $\mathcal{N} = 2$ supersymmetric gauge theory on S 4 is exactly evaluated in the presence of a supersymmetric ’t Hooft loop operator. The result we find — obtained using localization techniques — captures all perturbative quantum corrections as well as non-perturbative effects due to instantons and monopoles, which are supported at the north pole, south pole and equator of S 4. As a by-product, our gauge theory calculations successfully confirm the predictions made for ’t Hooft loops obtained from the calculation of topological defect correlators in Liouville/Toda conformal field theory.
Highlights
Supersymmetry — apart from being phenomenologically appealing for physics beyond the standard model — is a powerful symmetry which constraints the dynamics of gauge theories
The path integral of a general N = 2 supersymmetric gauge theory on S4 is exactly evaluated in the presence of a supersymmetric ’t Hooft loop operator
In this paper we evaluate the exact path integral which computes the expectation value of supersymmetric ’t Hooft loop operators in an arbitrary N = 2 supersymmetric gauge theory on S4 admitting a Lagrangian description
Summary
Supersymmetry — apart from being phenomenologically appealing for physics beyond the standard model — is a powerful symmetry which constraints the dynamics of gauge theories. Zequator(B, v) captures the contribution to the path integral of field configurations which are solutions to the Bogomolny equations in the presence of a singular monopole background labeled by the magnetic charge B, created by the ’t Hooft loop operator insertion. We introduce the main ingredients of the localization analysis in [2] that we require to calculate the exact expectation value of supersymmetric ’t Hooft operators in an arbitrary four dimensional N = 2 gauge theory on S4 admitting a Lagrangian description.7 Such a theory is completely characterized by the choice of a gauge group G and of a representation R of G under which the N = 2 hypermultiplet transforms, the N = 2 vectormultiplet transforming in the adjoint representation of G.
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