Renormalization of Supersymmetric Lifshitz Sigma Models

TL;DR

This paper investigates the renormalization properties of a supersymmetric Lifshitz sigma model in three dimensions, revealing its power-counting renormalizability and flow towards relativistic symmetry at low energies.

Contribution

It introduces a covariant heat kernel method for analyzing one-loop beta-functions in a bimetric target-space, advancing understanding of quantum critical supermembranes.

Findings

The sigma model is power-counting renormalizable.

The theory flows to a relativistic sigma model at low energies.

A covariant heat kernel method is developed for bimetric geometries.

Abstract

We study the renormalization of an N = 1 supersymmetric Lifshitz sigma model in three dimensions. The sigma model exhibits worldvolume anisotropy in space and time around the high-energy z = 2 Lifshitz point, such that the worldvolume is endowed with a foliation structure along a preferred time direction. In curved backgrounds, the target-space geometry is equipped with two distinct metrics, and the interacting sigma model is power-counting renormalizable. At low energies, the theory naturally flows toward the relativistic sigma model where Lorentz symmetry emerges. In the superspace formalism, we develop a heat kernel method that is covariantized with respect to the bimetric target-space geometry, using which we evaluate the one-loop beta-functions of the Lifshitz sigma model. This study forms an essential step toward a thorough understanding of the quantum critical supermembrane as a candidate high-energy completion of the relativistic supermembrane.