Beschreibung
Contribution of non-acyclic flat connections in Chern-Simons theory and invariants of 3-manifolds
Abstract:
Path integral of Chern-Simons theory on a closed 3-manifold gives a family of perturbative partition functions (effective BV actions induced on twisted de Rham cohomology) parametrized by the moduli space of flat connections. This family is horizontal with respect to the Grothendieck connection modulo a BV-exact term. I will outline how
(a) This family can be extended to a nonhomogeneous form over triples (kinetic flat connection, gauge-fixing flat connection, metric), satisfying a differential quantum master equation (i.e., is annihilated by an appropriate “Gauss-Manin” flat superconnection);
(b) One can extract from the extended partition function above a volume form on the smooth irreducible stratum of moduli space, whose cohomology class is metric-independent, and hence yields an invariant of a framed 3-manifold.
The talk is based on a joint work with Konstantin Wernli, arXiv:2510.18653, arxiv:2512.17638.