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General Relativity and the AKSZ Construction
G Canepa1, A S Cattaneo1, M Schiavina2,3
1Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zurich, Switzerland.
Communications in Mathematical Physics
|November 1, 2021
Summary
The AKSZ construction is applied to Einstein-Hilbert and Palatini-Cartan theories, yielding compatible BFV-BV descriptions for quantization with boundaries.
Area of Science:
- Theoretical Physics
- Mathematical Physics
Background:
- The Einstein-Hilbert and Palatini-Cartan theories are fundamental in describing gravity.
- Quantization of these theories, especially with boundaries, presents significant challenges.
Purpose of the Study:
- To apply the AKSZ construction to the BFV description of reduced phase spaces for Einstein-Hilbert and Palatini-Cartan theories.
- To develop a compatible BFV-BV description suitable for boundary quantization.
Main Methods:
- Application of the AKSZ (Alexandrov-Konstantinov-Schwartz-Zhibanov) construction.
- Utilizing the BFV (Batalin-Fradkin-Vilkovisky) formalism for describing reduced phase spaces.
- Analysis in arbitrary space-time dimensions greater than two.
Main Results:
- A BFV theory for the first-order formulation of Einstein-Hilbert theory was obtained.
- A BFV theory for Palatini-Cartan theory was derived, with partial implementation of the torsion-free condition.
- All resulting theories are BV versions of the same classical system on cylinders.
Conclusions:
- The AKSZ implementations provide a compatible BV-BFV description.
- This compatible description serves as a crucial starting point for quantization in the presence of a boundary.
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