Path-integral invariants in abelian Chern-Simons theory

Abstract

We consider the $U(1)$ Chern-Simons gauge theory defined in a general closed oriented 3-manifold $M$; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The nonperturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent $U(1)$ principal bundles over $M$; the different sectors of the configuration space are labelled by the elements of the first homology group of $M$ and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the extent of the nonperturbative contributions to the mean values. The functional integration is achieved in any 3-manifold $M$, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin-Turaev surgery invariants.

References in corpus (4)

• Topological boundary conditions in abelian Chern-Simons theory
• Classification of abelian spin Chern-Simons theories
• Functional integration and abelian link invariants
• Abelian link invariants and homology

Cited by in corpus (16)

• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Chern-Simons Invariants from Ensemble Averages
• Entanglement from Topology in Chern-Simons Theory
• Abelian BF theory and Turaev-Viro invariant
• A reciprocity formula from abelian BF and Turaev-Viro theories
• Lattice Chern-Simons-Maxwell Theory and its Chirality
• 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
• Five-dimensional fermionic Chern-Simons theory
• Renormalized Schwinger-Dyson functional
• Abelian Topological Order on Lattice Enriched with Electromagnetic Background
• 3D Topological Models and Heegaard Splitting I: Partition Function
• Gauge fixing and metric independence in topological quantum theories
• $U(1)$-Gauge Field Theories on $G_2$-Manifolds
• 3D Topological Models and Heegaard Splitting II: Pontryagin duality and Observables