Anomalies and symmetry fractionalization

Delmastro, Diego Gabriel; Gomis, Jaume; Hsin, Po-Shen; Komargodski, Zohar

doi:10.21468/SciPostPhys.15.3.079

SciPost Physics

Anomalies and symmetry fractionalization

Diego Delmastro, Jaume Gomis, Po-Shen Hsin, Zohar Komargodski

SciPost Phys. 15, 079 (2023) · published 5 September 2023

doi: 10.21468/SciPostPhys.15.3.079
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Abstract

We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified. Distinct choices of a fractionalization class can result in different values for the anomalies of $G$ if the theory has an anomaly involving $\Gamma$. Therefore, the computation of the 't Hooft anomaly for an ordinary symmetry $G$ generally requires first discovering the one-form symmetry $\Gamma$ of the physical system. We show that the multiple values of the anomaly for $G$ can be realized by twisted gauge transformations, since twisted gauge transformations shift fractionalization classes. We illustrate these ideas in QCD theories in diverse dimensions. We successfully match the anomalies of time-reversal symmetries in $2+1d$ gauge theories, across the different fractionalization classes, with previous conjectures for the infrared phases of such strongly coupled theories, and also provide new checks of these proposals. We perform consistency checks of recent proposals about two-dimensional adjoint QCD and present new results about the anomaly of the axial $\mathbb{Z}_{2N}$ symmetry in $3+1d$ ${\cal N}=1$ super-Yang-Mills. Finally, we study fractionalization classes that lead to 2-group symmetry, both in QCD-like theories, and in $2+1d$ $\mathbb{Z}_2$ gauge theory.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.3.079
TI  - Anomalies and symmetry fractionalization
PY  - 2023/09/05
UR  - https://www.scipost.org/SciPostPhys.15.3.079
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 3
SP  - 079
A1  - Delmastro, Diego Gabriel
AU  - Gomis, Jaume
AU  - Hsin, Po-Shen
AU  - Komargodski, Zohar
AB  - We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified. Distinct choices of a fractionalization class can result in different values for the anomalies of $G$ if the theory has an anomaly involving $\Gamma$. Therefore, the computation of the 't Hooft anomaly for an ordinary symmetry $G$ generally requires first discovering the one-form symmetry $\Gamma$ of the physical system. We show that the multiple values of the anomaly for $G$ can be realized by twisted gauge transformations, since twisted gauge transformations shift fractionalization classes. We illustrate these ideas in QCD theories in diverse dimensions. We successfully match the anomalies of time-reversal symmetries in $2+1d$ gauge theories, across the different fractionalization classes, with previous conjectures for the infrared phases of such strongly coupled theories, and also provide new checks of these proposals. We perform consistency checks of recent proposals about two-dimensional adjoint QCD and present new results about the anomaly of the axial $\mathbb{Z}_{2N}$ symmetry in $3+1d$ ${\cal N}=1$ super-Yang-Mills. Finally, we study fractionalization classes that lead to 2-group symmetry, both in QCD-like theories, and in $2+1d$ $\mathbb{Z}_2$ gauge theory.
ER  -

@Article{10.21468/SciPostPhys.15.3.079,
	title={{Anomalies and symmetry fractionalization}},
	author={Diego Delmastro and Jaume Gomis and Po-Shen Hsin and Zohar Komargodski},
	journal={SciPost Phys.},
	volume={15},
	pages={079},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.3.079},
	url={https://scipost.org/10.21468/SciPostPhys.15.3.079},
}

Cited by 11

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¹ ² Diego Gabriel Delmastro,
¹ ² Jaume Gomis,
³ Po-Shen Hsin,
⁴ Zohar Komargodski

Funders for the research work leading to this publication