Abstract
We study 1/2-BPS Wilson loop (WL) operators in maximally supersymmetric Yang-Mills theory (MSYM) on S5. Their vacuum expectation value (vev) can be computed exactly at large N thanks to supersymmetric localization. The holographic dual to MSYM on S5 is geometrically realized by a stack of N D4-branes with spherical worldvolume in ten dimensions. We compute the vev of the circular WL using holography by evaluating the partition function of a fundamental string in this background. Our focus is on the next-to-leading order correction to the string partition function which is composed of two parts; the dilaton coupling to the worldsheet and the one-loop fluctuations of the worldsheet itself. We face a variety of issues, some related to the presence of a non-constant dilaton, and others that are common to its AdS analogue. However, the universality of UV divergences as well as the importance of a proper choice of an IR regulator have been recently stressed in the literature. Inspired by this, we resolve our issues by first carefully treating the Weyl anomaly which receives contributions from the non-constant dilaton, and then by computing the ratio of our partition function and the one of a string in AdS4×CP3, which is dual to a 1/2-BPS WL in ABJM. Crucially, this approach yields a finite result which matches the corresponding ratio of WL vevs on the gauge theory side.
Highlights
Both study the vacuum structure of gauge theories using holography, and to further our understanding of holography itself
We study 1/2-BPS Wilson loop (WL) operators in maximally supersymmetric Yang-Mills theory (MSYM) on S5
Our focus is on the next-toleading order correction to the string partition function which is composed of two parts; the dilaton coupling to the worldsheet and the one-loop fluctuations of the worldsheet itself
Summary
The construction of a maximal supersymmetric gauge theory on the round sphere is nontrivial since introducing only the minimal coupling to the curved metric breaks supersymmetries. The partition function (2.3) and the consequent equation (2.5) appear in the matrix formulation of Chern-Simons theories on a three-dimensional sphere S3 [31, 46–48]. The gauge field on the other hand does vanish and the WL vev can be evaluated by taking the continuum limit and keeping only leading term in the large N expansion. The gauge field on the other hand does vanish and the WL vev can be evaluated by taking the continuum limit and keeping only leading term in the large N expansion5 This is the expectation value of a 12 -BPS Wilson loop located on the equator of the sphere S5 at large N but for any ’t Hooft coupling ξ.6. The exponential behaviour in the large ξ-expansion corresponds to (minus) the classical action of the dual string [30], cf. section 4.2, while the prefactor is encoded in the one-loop string partition function, cf. sections 5–6
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