Asymptotically flat boundary conditions for the $U(1)^3$ model for Euclidean Quantum Gravity

TL;DR

This paper investigates boundary conditions and asymptotic symmetries of a $U(1)^3$ gauge model for Euclidean quantum gravity, revealing limitations in defining certain symmetry generators compared to full general relativity.

Contribution

It analyzes the asymptotic symmetries of the $U(1)^3$ model, highlighting the absence of boost and rotation generators due to the lack of non-Abelian gauge components.

Findings

Well-defined generators for spacetime translations

Absence of boost and rotation generators

Comparison with full Euclidean GR shows crucial role of non-Abelian part

Abstract

A generally covariant $U(1)^3$ gauge theory describing the $G_N \to 0$ limit of Euclidean general relativity is an interesting test laboratory for general relativity, specially because the algebra of the Hamiltonian and diffeomorphism constraints of this limit is isomorphic to the algebra of the corresponding constraints in general relativity. In the present work, we study boundary conditions and asymptotic symmetries of the $U(1)^3$ model and show that while asymptotic spacetime translations admit well-defined generators, boosts and rotations do not. Comparing with Euclidean general relativity, one finds that exactly the non-Abelian part of the $SU(2)$ Gauss constraint which is absent in the $U(1)^3$ model plays a crucial role in obtaining boost and rotation generators.