2024/09/16 by Kim, Han-Miru, Mathieu, Philippe, Tagaris, Michail +1
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2409.10734
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 3-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.