Topological Quantum Field Theory via Chren-Simons Theory, part 1
Yifan Zhang, Ke Wu
TL;DR
This paper constructs a Topological Quantum Field Theory (TQFT) using Chern-Simons theory with compact Lie groups, interpreting cobordisms and spacetime fields through categorical frameworks.
Contribution
It provides a categorical construction of TQFT via Chern-Simons theory, clarifying the attachment to a point and the role of cobordisms and spacetime fields.
Findings
Categorical interpretation of TQFT and Chern-Simons theory
Construction of TQFT via cobordisms as cospans
Field of spacetime as spans
Abstract
To understand what does Chern-Simons with compact Lie group(does not like Dijkgraaf-Witten model with finite group in 3d) attach to a point, we first give a construction of Topological Quantum Field Theory(TQFT) via Chern-Simons theory in this paper. We discuss the Topological Quantum Field Theory and Chern-Simons theory via Category, then interpret the cobordism as cospan and field of space-time as span, which ultimately deduce the construction of TQFT.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics · Algebraic structures and combinatorial models