SciPost Submission Page
Wilson Loops and Spherical Branes
by Davide Astesiano, Pieter Bomans, Fridrik Freyr Gautason, Valentina Giangreco M. Puletti, Alexia Nix
Submission summary
| Authors (as registered SciPost users): | Pieter Bomans · Fridrik Freyr Gautason · Alexia Nix · Valentina Giangreco M Puletti |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2407.07830v1 (pdf) |
| Date submitted: | 2024-08-15 19:31 |
| Submitted by: | Nix, Alexia |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study 1/2-BPS Wilson loop operators in maximally supersymmetric Yang-Mills theory on $d$-dimensional spheres. Their vacuum expectation values can be computed at large $N$ through supersymmetric localisation. The holographic duals are given by back-reacted spherical D-branes. For $d\neq 4$, the resulting theories are non-conformal and correspondingly, the dual geometries do not possess an asymptotic AdS region. The main aim of this work is to compute the holographic Wilson loops by evaluating the partition function of a probe fundamental string and M2-brane in the dual geometry, focusing on the next-to-leading order. Along the way, we highlight a variety of issues related to the presence of a non-constant dilaton. In particular, the structure of the divergences of the one-loop partition functions takes a non-universal form in contrast to examples available in the literature. We devise a general framework to treat the divergences, successfully match the sub-leading scaling with $\lambda$ and $N$, and provide a first step towards obtaining the numerical prefactor.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1. Non-trivial test of holography in the non-conformal case, and non-trivial related analysis of quantization of strings and branes with proposal of regularization scheme.
2. Thorough analysis with many details, for sure of reference for future work on non-conformal precision holography
Weaknesses
There are no weaknesses.
Report
This paper contains results, obtained via holography, on Wilson loops expectation values at strong coupling, for Yang-Mills theories with maximal supersymmetry and defined on a d-dimensional sphere, for d=2,3,7. For such vevs results exact in the coupling are evailable in the literature, obtained at large N via supersymmetric localization.
The holographic calculation of this paper consists in the evaluation of the one-loop partition function for the string and M2-brane in the relevant dual geometry.
This case goes beyond the realm of the usual holographic dictionary, because the relevant field theory is not conformal. On the gravity side, this implies the presence of a running dilaton, something which plays a relevant role when discussing the UV finiteness of the partition function. The question of how to quantize strings and branes in backgrounds relevant in holography is definitively a relevant one, and it is also full of subtleties - mostly related to the evaluation of the relevant functional determinants - already in the conformal case. The thorough analysis of this paper addresses them in details (also with useful appendices containing standard and less standard lore on determinants calculations) and proposes a regularization scheme, which is also tested on previously treated cases. The agreement (or disagreement) with the results obtained from localization is also discussed in details, and the directions for future research are an interesting part of the manuscript.
For all these reasons, this work is certainly going to be of future reference for works on (precision) holography in the non-conformal case, and I am happy to recommend its publication on Scipost.
Requested changes
Very minor, on the Conclusions: in the first sentence, “we conduct a study into sub-leading corrections to the 1/2 BPS Wilson loop vev [...]” should better be “we conduct a study, via holography, of sub-leading, strong coupling corrections to the 1/2 BPS Wilson loop vev […]”. Also, to faciliate the comparison between localization and gravity results, (8.1) and (8.3), it would be perhaps useful to have them much closer in the text or on a Table.
Recommendation
Publish (meets expectations and criteria for this Journal)