Abstract
We classify bosonic $\mathcal{N}=(2,2)$ supersymmetric Wilson loops on arbitrary backgrounds with vector-like R-symmetry. These can be defined on any smooth contour and come in two forms which are universal across all backgrounds. We show that these Wilson loops, thanks to their cohomological properties, are all invariant under smooth deformations of their contour. At genus zero they can always be mapped to local operators and computed exactly with supersymmetric localisation. Finally, we find the precise map, under two-dimensional Seiberg-like dualities, of correlators of supersymmetric Wilson loops.
Highlights
Wilson loops are an important tool to understand the dynamics of gauge theories: they encode how an elementary excitation localized along the loop responds to the presence of a dynamical gauge field
Fayet-Iliopoulos and theta terms for the Abelian factors of the gauge group and twisted masses and background fluxes for the chiral multiplets can be added, enriching the parametric dependence of the results. In this theory a one-parameter family of Wilson loops with contours lying on latitudes of the round two-sphere were already considered in [53]: on the maximal circle the dimensionally reduced 16-BPS Wilson loop of three-dimensional N 1⁄4 2 theories is recovered, and the quantum expectation value of the whole family is independent from the latitude angle
We find that a single operator insertion is mapped to a combination of Wilson loops in different representations
Summary
Wilson loops are an important tool to understand the dynamics of gauge theories: they encode how an (infinitely massive) elementary excitation localized along the loop responds to the presence of a dynamical gauge field. Wε 1⁄4 trP exp iðAa þ faε σ þ faε σ Þx_adt; Wε 1⁄4 trP exp iðAa þ faεσ þ faεσ ̃ Þx_adt; ð1Þ where σ and σare the scalar fields in the gauge supermultiplet and the couplings fa and fa are defined in (9) and (10) These loops are 14-BPS, and the analysis of the preserved supersymmetries extends to the case of a general Riemann surface. Fayet-Iliopoulos and theta terms for the Abelian factors of the gauge group and twisted masses and background fluxes for the chiral multiplets can be added, enriching the parametric dependence of the results In this theory a one-parameter family of Wilson loops with contours lying on latitudes of the round two-sphere were already considered in [53]: on the maximal circle the dimensionally reduced 16-BPS Wilson loop of three-dimensional N 1⁄4 2 theories is recovered, and the quantum expectation value of the whole family is independent from the latitude angle. V we determine how correlators of Wilson loops are mapped under Seiber-like dualities and provide explicit examples
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