Abstract
We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in mathcal{N} = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.
Highlights
The ’t Hooft line operator, defined by a singular Dirac monopole boundary condition Fμν dxμ ∧ dxν ∼ B 2 volS2(B: magnetic charge) (1.1)on a gauge field, is an interesting disorder operator that universally exists in all fourdimensional (4d) gauge theories
We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories
In this paper we calculated by supersymmetric localization the expectation values of ’t Hooft operators on S1 × R3 in theories with gauge groups U(N ), SO(N ) and USp(N )
Summary
The ’t Hooft line operator, defined by a singular Dirac monopole boundary condition. on a gauge field, is an interesting disorder operator that universally exists in all fourdimensional (4d) gauge theories. In our previous paper [13] that considered the U(N ) gauge theory with hypermultiplets in the fundamental representation (SQCD), we explored, by extending a result in [14], the relation between wall-crossing in the SQMs and the ordering of ’t Hooft operators along the line (in R3) on which the operators are inserted. The gauge theories whose matter hypermultiplets are in this representation will be referred to as SQCDs. We extend the relation between wall-crossing and operator ordering to the cases with non-minimal higher charges. To read off the SQMs we will realize the gauge theories, ’t Hooft operators, and monopole screening in D2-D4-NS5-D6-brane systems, together with an orientifold 4- or 6-plane for the SO(N ) or USp(N ) gauge group. We discuss the subtleties exhibited by these correlators and discuss their possible interpretations
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