We undertake a detailed study of the gaugings of two-dimensional Yang–Mills theory by its intrinsic charge conjugation 0-form and centre 1-form global symmetries, elucidating their higher algebraic and geometric structures, as well as the meaning of dual lower form symmetries. Our derivations of orbifold gauge theories make use of a combination of standard continuum path integral methods, networks of topological defects, and techniques from higher gauge theory. We provide a unified description of higher and lower form gauge fields for a p-form symmetry in the geometric setting of p-gerbes, and derive reverse orbifolds by the dual <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11005_2025_1905_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">$(-1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-form symmetries. We identify those orbifolds in which charge conjugation symmetry is spontaneously broken, and relate the breaking to mixed anomalies involving <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11005_2025_1905_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">$(-1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-form symmetries. We extend these considerations to gaugings by the non-invertible 1-form symmetries of two-dimensional Yang–Mills theory by introducing a notion of generalized <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11005_2025_1905_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>θ</mi> </math></EquationSource> </InlineEquation>-angle.

Higher form symmetries and orbifolds of two-dimensional Yang–Mills theory

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发表日期：

2025年1月31日

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Leonardo Santilli,
Richard J. Szabo

摘要

We undertake a detailed study of the gaugings of two-dimensional Yang–Mills theory by its intrinsic charge conjugation 0-form and centre 1-form global symmetries, elucidating their higher algebraic and geometric structures, as well as the meaning of dual lower form symmetries. Our derivations of orbifold gauge theories make use of a combination of standard continuum path integral methods, networks of topological defects, and techniques from higher gauge theory. We provide a unified description of higher and lower form gauge fields for a p-form symmetry in the geometric setting of p-gerbes, and derive reverse orbifolds by the dual $(-1)$ $(- 1)$ -form symmetries. We identify those orbifolds in which charge conjugation symmetry is spontaneously broken, and relate the breaking to mixed anomalies involving $(-1)$ $(- 1)$ -form symmetries. We extend these considerations to gaugings by the non-invertible 1-form symmetries of two-dimensional Yang–Mills theory by introducing a notion of generalized $\theta $ $θ$ -angle.