Chern-Simons theory, decomposition, and the A model
arXiv:2406.18633 · doi:10.1007/JHEP10(2024)112
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.
arXiv comment25 pages, LaTeX; v2: minor writing updates
References in corpus (20)
- String Theory Dynamics In Various Dimensions
- Generalized Global Symmetries
- D-Branes And K-Theory
- Evidence for Heterotic - Type I String Duality
- Open Strings
- D-branes in the WZW model
- Cluster decomposition, T-duality, and gerby CFT's
- GLSM's for gerbes (and other toric stacks)
- Open Strings and D-branes in WZNW model
- String compactifications on Calabi-Yau stacks
- Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory
- Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond -ality
- Decomposition, condensation defects, and fusion
- Undoing decomposition
- D-branes, B fields, and Ext groups
- Lifetimes of (near) eternal false vacua
- General aspects of heterotic string compactifications on stacks and gerbes
- Categorical Equivalence and the Renormalization Group
- Decomposition in Chern-Simons theories in three dimensions
- Three-dimensional orbifolds by 2-groups