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Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit
by Zheng Zhou, Yin-Chen He
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Zheng Zhou |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2205.07897v2 (pdf) |
| Date accepted: | 2023-07-10 |
| Date submitted: | 2023-06-01 03:02 |
| Submitted by: | Zhou, Zheng |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study the slightly broken higher-spin currents in various CFTs with $\mathrm{U}(1)$ gauge field, including the tricritical QED, scalar QED, fermionic QED and QED-Gross-Neveu-Yukawa theory. We calculate their anomalous dimension by making use of the classical non-conservation equation and the equations of motion. We find a logarithmic asymptotic behaviour ($\gamma_s\sim 16/(N\pi^2) \log s $) of the anomalous dimension at large spin $s$, which is different from other interacting CFTs without gauge fields and may indicate certain unique features of gauge theories. We also study slightly broken higher-spin currents of the $\mathrm{SU}(N)_1$ WZW model at $d=2+\epsilon$ dimensions by formulating them as the QED theory, and we again find its anomalous dimension has a logarithmic asymptotic behaviour with respect to spin. This result resolves the mystery regarding the mechanism of breaking higher spin currents of Virasoro symmetry at $d=2+\epsilon$ dimensions, and may be applicable to other interesting problems such as the $2+\epsilon$ expansion of Ising CFT.
Author comments upon resubmission
We appreciate the positive evaluation of both Referees. We also thank their critical comments that are important to understanding the problems in concern. These points are addressed in the attached reply. Thanks to the comments of the Referees, we have made improvements to the paper. The revisions made are listed below.
We give a point-by-point response to the comments of all Referees. We hope that with the changes made, the current manuscript will be considered suitable for further consideration in SciPost Physics.
List of changes
* We have added discussion on the simultaneous limits that we take for $s$ and $N$ in Section 6;
* We have added discussion to clarify the absence of divergence operator in 2d and its reappearance in $(2+\epsilon)$d in Section 5;
* We have added relevant references for lightcone bootstrap mentioned by Referee 1;
* We have corrected several typos mentioned by Referee 2;
* We have added discussion to clarify the generalisation of $\mathrm{SU}(N)_1$ WZW from 2d to $(2+\epsilon)$d in Section 5.
Published as SciPost Phys. 15, 072 (2023)