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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
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Summary
This summary is machine-generated.

The AKSZ construction is applied to Einstein-Hilbert and Palatini-Cartan theories, yielding compatible BFV-BV descriptions for quantization with boundaries.

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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.