On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics

Abstract

We revisit the localization computation of the expectation values of 't Hooft operators in $\mathcal{N}=2^{\ast }$ SU(N) theory on ${\mathbb{R}}^3\times S^1$. We show that the part of the answer arising from "monopole bubbling" on ${\mathbb{R}}^3$ can be understood as an equivariant integral over a Kronheimer-Nakajima moduli space of instantons on an orbifold of ${\mathbb{C}}^2$. 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. In addition, we present a Type IIB construction -- involving D1-D3-NS5-branes -- for monopole bubbling in $\mathcal{N}=2^{\ast }$ SU(N) SYM and demonstrate how the quiver quantum mechanics arises in this brane picture.

43+ 41 pages, 14 figures

References in corpus (9)

• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Witten Index and Wall Crossing
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Instantons on Gravitons
• Superconformal Index with Duality Domain Wall
• The 't Hooft-Polyakov Monopole in the Presence of a 't Hooft Operator
• N=2 quiver gauge theories on A-type ALE spaces
• Singular Monopoles via the Nahm Transform
• Equivariant volumes of non-compact quotients and instanton counting

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