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arXiv · 2406.18633

Chern-Simons theory, decomposition, and the A model

Tony Pantev·Eric Sharpe·Xingyang Yu
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Abstract

In this paper, we discuss how gauging one-form symmetries in Chern-Simons theories is implemented in an A-twisted topological open string theory. For example, the contribution from a fixed H/Z bundle on a three-manifold M, arising in a BZ gauging of H Chern-Simons, for Z a finite subgroup of the center of H, is described by an open string worldsheet theory whose bulk is a sigma model with target a Z-gerbe (a bundle of one-form symmetries) over T^* M, of characteristic class determined by the H/Z bundle. We give a worldsheet picture of the decomposition of one-form-symmetry-gauged Chern-Simons in three dimensinos, and we describe how a target-space constraint on bundles arising in the gauged Chern-Simons theory has a natural worldsheet realization. Our proposal provides examples of the expected correspondence between worldsheet global higher-form symmetries, and target-space gauged higher-form symmetries.

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Tony Pantev, Eric Sharpe, Xingyang Yu. 2024-06-26. Chern-Simons theory, decomposition, and the A model. https://doi.org/10.1007/jhep10(2024)112

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