Anomalous Breaking of Anisotropic Scaling Symmetry in the Quantum Lifshitz Model

TL;DR

This paper investigates the quantum Lifshitz model's anisotropic scale symmetry breaking, computing its central charges and revealing that one vanishes, with implications for strongly coupled non-relativistic theories with geometric duals.

Contribution

It provides the first explicit calculation of the central charges associated with anisotropic scale symmetry breaking in the quantum Lifshitz model.

Findings

One central charge vanishes in the quantum Lifshitz model.

The vanishing of this charge also occurs in certain strongly coupled theories with geometric duals.

Abstract

In this note we investigate the anomalous breaking of anisotropic scaling symmetry in a non-relativistic field theory with dynamical exponent z=2. On general grounds, one can show that there exist two possible "central charges" which characterize the breaking of scale invariance. Using heat kernel methods, we compute these two central charges in the quantum Lifshitz model, a free field theory which is second order in time and fourth order in spatial derivatives. We find that one of the two central charges vanishes. Interestingly, this is also true for strongly coupled non-relativistic field theories with a geometric dual described by a metric and a massive vector field.