Topological Quantum Field Theories from Compact Lie Groups
read the original abstract
It is a long-standing question to extend the definition of 3-dimensional Chern-Simons theory to one which associates values to 1-manifolds with boundary and to 0-manifolds. We provide a solution in case the gauge group is a torus. We also develop from different points of view an associated 4-dimensional invertible topological field theory which encodes the anomaly of Chern-Simons. Finite gauge groups are also revisited, and we describe a theory of "finite path integrals" as a general construction for a certain class of finite topological field theories. Topological pure gauge theories in lower dimension are presented as a warm-up.
This paper has not been read by Pith yet.
Forward citations
Cited by 6 Pith papers
-
The Algebra of Categorical Spectra
Constructs the tensor product of categorical spectra and uses stability phenomena to derive the cobordism hypothesis with singularities categorically from the ordinary cobordism hypothesis.
-
A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects
A geometric construction of untwisted 3d Dijkgraaf-Witten TQFT with defects via gauge groupoid representations and fibrant spans of groupoids.
-
Categorical Symmetries via Operator Algebras
The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra,...
-
Candidate Gaugings of Categorical Continuous Symmetry
Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.
-
Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation
Illustrates relations among gauging methods for invertible symmetries in 3D TQFTs and proves Morita equivalence of zested orbifold data for related symmetries.
-
Topological symmetry in quantum field theory
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.