Quantum Chern-Simons Theories on Cylinders: BV-BFV Partition Functions

Area of Science:

• Theoretical Physics
• Mathematical Physics
• Quantum Field Theory

Background:

• Chern-Simons theory is a fundamental concept in topological quantum field theory.
• The BV-BFV formalism provides a framework for quantizing gauge theories on manifolds with boundaries.
• Understanding partition functions is key to quantizing field theories.

Purpose of the Study:

• To compute partition functions of Chern-Simons type theories on cylindrical spacetimes.
• To connect the BV-BFV effective action with Hamilton-Jacobi actions.
• To explore implications for conformal field theory and gravity.

Main Methods:

• Utilizing the Batalin-Vilkovisky-French-Vieu (BV-BFV) formalism.
• Computing partition functions for Chern-Simons theories on cylinder manifolds.
• Identifying the physical part of the BV-BFV effective action.

Main Results:

• The physical part of the BV-BFV effective action was identified with the Hamilton-Jacobi action.
• This connection holds without quantum corrections for specific residual field choices.
• A version of the Chern-Simons-Wess-Zumino-Witten (CS-WZW) correspondence was established for certain geometries.
• A relationship between Chern-Simons partition functions and Kodaira-Spencer gravity (BCOV theory) was found for specific cylinder configurations.

Conclusions:

• The study provides a BV-BFV quantum perspective on semiclassical results in theoretical physics.
• The findings bridge concepts in topological field theory, conformal field theory, and quantum gravity.
• The BV-BFV formalism offers a powerful tool for quantizing gauge theories with boundary conditions.