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

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arxiv 2205.07897 v2 pith:4Q4RKETC submitted 2022-05-16 hep-th cond-mat.stat-mechcond-mat.str-el

Zheng Zhou , Yin-Chen He This is my paper · ORCID
classification hep-thcond-mat.stat-mechcond-mat.str-el
keywords anomalousbrokencurrentsdimensionepsilongaugehigher-spinslightly
verification ladder T0 review T1 audit T2 compute T3 formal

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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Coupled minimal models revisited II: Constraints from permutation symmetry

    hep-th 2024-12 accept novelty 7.0 of 10

    For coupled large-m minimal models with N=5,6,7, every permutation-charged current below spin 10 acquires an anomalous dimension, so the IR fixed points show no extended chiral algebra in that range.

  2. On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions

    hep-th 2026-01 conditional novelty 6.0 of 10

    The d→2 Wilson-Fisher limit is proposed to be strictly larger than the 2d Ising CFT, which emerges as a unitary subsector after negative-multiplicity operators cancel exactly.

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