Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit

Zhou, Zheng; He, Yin-Chen

doi:10.21468/SciPostPhys.15.2.072

SciPost Physics

Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit

Zheng Zhou, Yin-Chen He

SciPost Phys. 15, 072 (2023) · published 29 August 2023

doi: 10.21468/SciPostPhys.15.2.072
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Abstract

We study the slightly broken higher-spin currents in various CFTs with 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 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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.2.072
TI  - Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit
PY  - 2023/08/29
UR  - https://scipost.org/SciPostPhys.15.2.072
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 2
SP  - 072
A1  - Zhou, Zheng
AU  - He, Yin-Chen
AB  - We study the slightly broken higher-spin currents in various CFTs with 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 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.
ER  -

@Article{10.21468/SciPostPhys.15.2.072,
	title={{Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit}},
	author={Zheng Zhou and Yin-Chen He},
	journal={SciPost Phys.},
	volume={15},
	pages={072},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.2.072},
	url={https://scipost.org/10.21468/SciPostPhys.15.2.072},
}

Cited by 3

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¹ ² Zheng Zhou,
¹ Yin-Chen He

Funders for the research work leading to this publication