Modified Villain formulation of Abelian Chern-Simons theory

Jacobson, Theodore; Sulejmanpasic, Tin

Abstract

We formulate U(1)k Chern-Simons theory on a Euclidean spacetime lattice using the modified Villain approach. Various familiar aspects of continuum Chern-Simons theory such as level quantization, framing, the discrete 1-form symmetry and its ’t Hooft anomaly, as well as the electric charge of monopole operators are manifest in our construction. The key technical ingredient is the cup product and its higher generalizations on the (hyper-)cubic lattice, which recently appeared in the literature. All unframed Wilson loops are projected out by a peculiar subsystem symmetry, leaving topological, ribbonlike Wilson loops which have the correct correlation functions and topological spins expected from the continuum theory. Our action can be obtained from a new definition of the theta term in four dimensions which improves upon previous constructions within the modified Villain approach. This bulk action coupled to background fields for the 1-form symmetry is given by the Pontryagin square, which provides anomaly inflow directly on the lattice.

Citation

Jacobson, T., & Sulejmanpasic, T. (2023). Modified Villain formulation of Abelian Chern-Simons theory. Physical Review D, 107(12), Article 125017. https://doi.org/10.1103/physrevd.107.125017

• Journal Article Type: Article
• Acceptance Date: May 31, 2023
• Online Publication Date: Jun 16, 2023
• Publication Date: 2023-06
• Deposit Date: Jan 4, 2024
• Publicly Available Date: Jan 4, 2024
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 107
• Issue: 12
• Article Number: 125017
• DOI: https://doi.org/10.1103/physrevd.107.125017
• Public URL: https://durham-repository.worktribe.com/output/2079602