Three-manifold invariant from functional integration

Abstract

We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism, we sum over the inequivalent U(1) principal bundles over the manifold and, for each bundle, we integrate over the gauge orbits of the associated connection 1- forms. The result of the functional integration is compared with the abelian U(1) Reshetikhin-Turaev surgery invariant.

References in corpus (2)

• Higher dimensional abelian Chern-Simons theories and their link invariants
• Localization in Abelian Chern-Simons Theory

Cited by in corpus (9)

• Path-integral invariants in abelian Chern-Simons theory
• Abelian BF theory and Turaev-Viro invariant
• A reciprocity formula from abelian BF and Turaev-Viro theories
• Abelian Turaev-Virelizier theorem and $U(1)$ BF surgery formulas
• Flat connections in three-manifolds and classical Chern-Simons invariant
• Schwinger-Dyson functional in Chern-Simons theory
• 3D Topological Models and Heegaard Splitting I: Partition Function
• 3D Topological Models and Heegaard Splitting II: Pontryagin duality and Observables
• Gauge fixing and metric independence in topological quantum theories