Stacks in Einstein Gravity and a Stacky Equivalence of 3D Quantum Gravity with Gauge Theory
Abstract
In this paper, we examine stacky structures in Einstein's theory of gravity. In brief, we first give a construction of the moduli stack of solutions to (vacuum) Einstein field equations on -dimensional spacetimes, with vanishing cosmological constant. Using a similar approach, we also study Einstein's gravity on families of manifolds and define another stack encoding this situation as well. Secondly, we focus on the gauge theoretical interpretation of 3D gravity and the concept of equivalence of 3D quantum gravity with gauge theory. By equivalence, we essentially mean the existence of an isomorphism between the phase spaces of 3D gravity and the associated gauge theory. In this regard, we show that once it exists, the equivalence induces an isomorphism between the corresponding moduli stacks.
Cite
@article{arxiv.1907.00665,
title = {Stacks in Einstein Gravity and a Stacky Equivalence of 3D Quantum Gravity with Gauge Theory},
author = {Kadri İlker Berktav},
journal= {arXiv preprint arXiv:1907.00665},
year = {2023}
}
Comments
30 pages; 1) the manuscript's organization broadly changed; 2) the current version focuses only on the main results concerning stacky constructions and avoids some of the survey parts presented in the previous version; 3) some additional arguments, corrections, and improvements; 4) part of the original discussion is extended to the families of manifolds. Comments are very welcome