Line operators in U(1|1) Chern-Simons theory

Journal article

We analyze the non-semisimple category of line operators in Chern-Simons gauge theories based off the Lie superalgebra gl(1|1). Our proposal is that the category of line operators C can be identified with the derived category of modules for a boundary vertex operator algebra V realized as a certain infinite-order simple current extension of the affine current algebra V (gl(1|1)) by boundary monopole operators. By translating this simple current extension of V (gl(1|1)) to the unrolled, restricted quantum group U E (gl(1|1)), we show that our category of line operators admits a second description in terms of a quasi-quantum group A realized by uprolling. We also compare our results across an expected physical duality with the cyclic orbifold of a free, B-twisted hypermultiplet and find a slight discrepancy at the level of braiding and associator. We end with a detailed analysis of coupling to background flat GL(1, C) connections and the resulting category of non-genuine line operators.

Authors: Garner, N; Niu, W

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Communications in Mathematical Physics
• Volume: 407
• Issue: 3
• Article number: 47
• Publication date: 2026-02-05
• Acceptance date: 2025-12-23
• DOI: 10.1007/s00220-025-05546-5
• EISSN: 1432-0916
• ISSN: 0010-3616
• Language: English
• Keywords: non-semisimple TQFT; logarithmic VOA; quantum supergroups; braided tensor categories