Self-dual formulations of d=3 gravity theories in the path-integral framework

TL;DR

This paper explores the quantum relationships between various self-dual models of three-dimensional gravity, establishing dualities and gauge invariances through path-integral methods.

Contribution

It introduces identities between generating functionals of different order self-dual models in 3D gravity, revealing their quantum dualities and gauge invariance.

Findings

Established dual maps among vacuum expectation values

Verified gauge invariance consistency in dual models

Connected models of increasing order via path-integral identities

Abstract

We study the connection, at the quantum level, between d=2+1 dimensional self-dual models with actions of growing (from first to fourth) order, governing the dynamics of helicity +2 (or -2) massive excitations. We obtain identities between generating functionals of the different models using the path-integral framework, this allowing to establish dual maps among relevant vacuum expectation values. We check consistency of these v.e.v.'s with the gauge invariance gained in each mapping.