Abstract
We revisit the localization computation of the expectation values of ’t Hooft operators in mathcal{N} = 2* SU(N) theory on ℝ3 × S1. We show that the part of the answer arising from “monopole bubbling” on ℝ3 can be understood as an equivariant integral over a Kronheimer-Nakajima moduli space of instantons on an orbifold of ℂ2. It can also be described as a Witten index of a certain supersymmetric quiver quantum mechanics with mathcal{N} = (4, 4) supersymmetry. The map between the defect data and the quiver quantum mechanics is worked out for all values of N. For the SU(2) theory, we compute several examples of these line defect expectation values using the Witten index formula and confirm that the expressions agree with the formula derived by Okuda, Ito and Taki [16]. In addition, we present a Type IIB construction — involving D1-D3-NS5-branes — for monopole bubbling in mathcal{N} = 2* SU(N) SYM and demonstrate how the quiver quantum mechanics arises in this brane picture.
Highlights
’t Hooft-Wilson defects are the simplest class of non-local operators in gauge theories and have been studied from various perspectives, starting with the pioneering work of ’t Hooft [65, 68, 69]
We present a Type IIB construction — involving D1-D3-NS5-branes — for monopole bubbling in N = 2∗ SU(N ) SYM and demonstrate how the quiver quantum mechanics arises in this brane picture
In this paper we study ’t Hooft defects in four-dimensional N = 2∗ SU(N ) gauge theory on R3 × S1, where the defect is inserted at the origin of R3
Summary
’t Hooft-Wilson defects are the simplest class of non-local operators in gauge theories and have been studied from various perspectives, starting with the pioneering work of ’t Hooft [65, 68, 69]. The path integral expression for the vev TB (γm) can be reduced to an integral over the moduli space of singular monopoles on R3 with an ’t Hooft defect of charge B at the origin and asymptotic charge γm at spatial infinity. We will denote this space M(B, γm, X∞). This allows one to compute precise equivariant expressions for coefficients of the “Abelianization Maps” introduced by Bullimore, Dimofte and Gaiotto [6]
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