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

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 massive excitations. We obtain identities between generating functionals of the different models using the path-integral framework, this allowing us to establish dual maps among relevant vacuum expectation values. We check consistency of these vacuum expectation values with the gauge invariance gained in each mapping.