Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

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.

Section: Jhep03(2022)018mentioning

confidence: 99%

Precision holography for 5D Super Yang-Mills

Gautason

Puletti

2022

“…We see that both anomaly coefficients are generally independent of each other. Owing to recent work on the constraint of supersymmetry on defect anomaly coefficients [45,46], one could hope that supersymmetry would directly relate these coefficients. From our analysis, we see that to get a direct relation, we should ask that all contributions from the spin-2…”

Section: Relating C Ddd and C Ddmentioning

confidence: 99%

A sum rule for boundary contributions to the trace anomaly

Herzog

Schaub

2022

In the context of boundary conformal field theory, we derive a sum rule that relates two and three point functions of the displacement operator. For four dimensional conformal field theory with a three dimensional boundary, this sum rule in turn relates the two boundary contributions to the anomaly in the trace of the stress tensor. We check our sum rule for a variety of free theories and also for a weakly interacting theory, where a free scalar in the bulk couples marginally to a generalized free field on the boundary.

“…worthwhile to revisit the O(N ) model discussed in a recent paper [56] that admits various non-trivial boundary conditions and supersymmetric theories with defects [43,[89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106][107] from the viewpoint of this paper. (See also [108][109][110][111][112][113] for related works.)…”

Section: Jhep05(2021)074mentioning

confidence: 99%

Free energy and defect C-theorem in free scalar theory

Nishioka

Sato

2021

We describe conformal defects of p dimensions in a free scalar theory on a d-dimensional flat space as boundary conditions on the conformally flat space ℍp+1× 𝕊d−p−1. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace ℍp+1 which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the non-monodromy defects, showing Neumann boundary conditions are associated with non-trivial defects. We check this observation by calculating the difference of the free energies on ℍp+1× 𝕊d−p−1 between Dirichlet and Neumann boundary conditions. We also examine the defect RG flows from Neumann to Dirichlet boundary conditions and provide more support for a conjectured C-theorem in defect CFTs.