Renormalization of the Einstein-Cartan Theory in First-Order Form

TL;DR

This paper investigates the renormalization properties of Einstein-Cartan theory in first-order form, employing the Batalin-Vilkovisky formalism and background field method to analyze gauge invariance and compute one-loop self-energy corrections.

Contribution

It provides a detailed analysis of the renormalizability of Einstein-Cartan theory using advanced gauge-invariant techniques and computes the one-loop self-energy of the tetrad field.

Findings

Demonstrates gauge invariance of the background effective action.

Derives Ward identities reflecting the symmetries of the theory.

Calculates the one-loop self-energy of the tetrad field.

Abstract

We examine the Einstein-Cartan (EC) theory in first-order form, which has a diffeomorphism as well as a local Lorentz invariance. We study the renormalizability of this theory in the framework of the Batalin-Vilkovisky formalism, which allows for a gauge invariant renormalization. Using the background field method, we discuss the gauge invariance of the background effective action and analyze the Ward identities which reflect the symmetries of the EC theory. As an application, we compute, in a general background gauge, the self-energy of the tetrad field at one-loop order.