For semisimple Lie algebra targets
For discrete group targets
For discrete 2-group targets
For Lie 2-algebra targets
For targets extending the super Poincare Lie algebra
(such as the supergravity Lie 3-algebra, the supergravity Lie 6-algebra)
Chern-Simons-supergravity
for higher abelian targets
for symplectic Lie n-algebroid targets
for the -structure on the BRST complex of the closed string:
higher dimensional Chern-Simons theory
topological AdS7/CFT6-sector
physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
Where ordinary 3d Chern-Simons theory is given by an action functional with values in the circle group on a space of special unitary group-principal connections, its “analytic continuation”(Gukov 03, Witten 10) instead is defined on complex special linear group-principal connections and its values are elements in (see also at Chern-Simons theory with complex gauge group).
The Wilson line quantum observables of analytically continued Chern-Simons theory are accordingly analytic continuations of knot invariants (Garoufalidis 07).
Discussion of the phase space with its complex symplectic form is in Gukov 03, section 2.2
Sergei Gukov, Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial, Commun.Math.Phys. 255 (2005) 577-627 (arXiv:hep-th/0306165)
Stavros Garoufalidis, Chern-Simons theory, analytic continuation and arithmetic (arXiv:0711.1716)
Edward Witten, Analytic Continuation Of Chern-Simons Theory, Chern–Simons Gauge Theory, 20, 347-446. (arXiv:1001.2933)
Tudor Dimofte, Quantum Riemann Surfaces in Chern-Simons Theory (arXiv:1102.4847)
Edward Witten, Two Lectures On The Jones Polynomial And Khovanov Homology (arXiv:1401.6996)
Last revised on December 26, 2019 at 00:16:21. See the history of this page for a list of all contributions to it.