Supergravity in $2+\epsilon$ Dimensions

TL;DR

This paper investigates supergravity in 2+epsilon dimensions, computing one-loop divergences, identifying a fixed point, and analyzing operator renormalization, providing insights into quantum properties near two dimensions.

Contribution

It introduces a gauge fixing method that isolates conformal modes and studies the renormalization of operators in supergravity close to two dimensions.

Findings

Explicit one-loop divergence calculation

Discovery of a nontrivial fixed point

Renormalization of gravitationally dressed operators

Abstract

Supergravity theory in $2+\epsilon$ dimensions is studied. It is invariant under supertransformations in 2 and 3 dimensions. One-loop divergence is explicitly computed in the background field method and a nontrivial fixed point is found. In quantizing the supergravity, a gauge fixing condition is devised which explicitly isolates conformal and superconformal modes. The renormalization of the gravitationally dressed operators is studied and their anomalous dimensions are computed. Problems to use the dimensional reduction are also examined.