# Holographic S-fold theories at one loop

### Submission summary

 As Contributors: Connor Behan Arxiv Link: https://arxiv.org/abs/2202.05261v4 (pdf) Date accepted: 2022-04-21 Date submitted: 2022-04-12 14:44 Submitted by: Behan, Connor Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

A common feature of tree-level holography is that a correlator in one theory can serve as a generating function for correlators in another theory with less continuous symmetry. This is the case for a family of 4d CFTs with eight supercharges which have protected operators dual to gluons in the bulk. The most recent additions to this family were defined using S-folds which combine a spatial identification with an action of the S-duality group in type IIB string theory. Differences between these CFTs which have a dynamical origin first become manifest at one loop. To explore this phenomenon at the level of anomalous dimensions, we use the AdS unitarity method to bootstrap a one-loop double discontinuity. Compared to previous studies, the subsequent analysis is performed without any assumption about which special functions are allowed. Instead, the Casimir singular and Casimir regular terms are extracted iteratively in order to move from one Regge trajectory to the next. Our results show that anomalous dimensions in the presence of an S-fold are no longer rational functions of the spin.

Published as SciPost Phys. 12, 149 (2022)

### List of changes

In accordance with the referee comments:
1. Section 4.3.3 has been added to report spin-1 and spin-2 anomalous dimensions for the k=2 S-fold.
2. Section 4.5 has been added to discuss the one-loop Mellin amplitude.
3. A paragraph has been added to section 5 about which complications might arise in other theories.

4. There are now a few more citations to prior work on holographic correlators.
5. The main results previously had a sign error and a more substantial coefficient error in the k=4 case. These have been corrected.

### Submission & Refereeing History

#### Published as SciPost Phys. 12, 149 (2022)

Resubmission 2202.05261v4 on 12 April 2022
Submission 2202.05261v1 on 21 February 2022

## Reports on this Submission

### Report

With the new corrections, I think the draft is ready for submission. I think it would be nice if the $k>2$ case could also be given an exact expression, but perhaps that will require new methods.

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