Wall-crossing and operator ordering for 't Hooft operators in N=2 gauge theories

Abstract

We study half-BPS 't Hooft line operators in 4d $\mathcal{N}=2$ $U(N)$ gauge theories on $S^1\times {\mathbb{R}}^3$ with an $\Omega$-deformation. The recently proposed brane construction of 't Hooft operators shows that non-perturbative contributions to their correlator are identified with the Witten indices of quiver supersymmetric quantum mechanics. For the products of minimal 't Hooft operators, a chamber in the space of Fayet-Iliopoulos parameters in the quantum mechanics corresponds to an ordering of the operators inserted along a line. These considerations lead us to conjecture that the Witten indices can be read off from the Moyal products of the expectation values of the minimal 't Hooft operators, and also that wall-crossing occurs in the quantum mechanics only when the ordering of the operators changes. We confirm the conjectures by explicitly computing the Witten indices for the products of two and three minimal 't Hooft operators in all possible chambers.

57 pages, many figures; comments added, statements clarified, typos fixed, version in JHEP

References in corpus (6)

• Witten Index and Wall Crossing
• Ω-deformation and quantization
• Gauge Theory Wilson Loops and Conformal Toda Field Theory
• On Monopole Bubbling Contributions to 't Hooft Loops
• 't Hooft Defects and Wall Crossing in SQM
• Index-Like Theorems from Line Defect Vevs

Cited by in corpus (6)

• A slow review of the AGT correspondence
• ABCD of 't Hooft operators
• S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories
• $\mathcal{N}=4$ line defect correlators of type BCD
• SUSY localization for Coulomb branch operators in omega-deformed 3d N=4 gauge theories