Work

U(1)n Chern–Simons theory: Partition function, reciprocity formula and Chern–Simons duality

Year: 2025

Type: article

Abstract: The U(1) Chern–Simons theory can be extended to a topological U(1)n theory by taking a combination of Chern–Simons and BF actions, the mixing being achieved with the help of a collection of integer coupling constants. Based on the Deligne–Beilinson cohomology, a partition function can then be computed for such a U(1)n Chern–Simons theory. This partition function is clearly a topological invariant of the closed oriented three-manifold on which the theory is defined. Then, by applying a reciprocity formula a new expression of this invariant is obtained which should be a Reshetikhin–Turaev invariant. Finally, a duality between U(1)n Chern–Simons theories is demonstrated.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0239253

Authors: Han-Miru Kim, Philippe Mathieu, Michail Tagaris, Frank Thuillier

Institutions: ETH Zurich, University of Zurich, Centre National de la Recherche Scientifique, Laboratoire d'Annecy de Physique Théorique

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green