Membranes at Quantum Criticality

TL;DR

This paper develops a quantum membrane theory at Lifshitz criticality that reproduces string partition functions, involving novel worldvolume matter and gravity theories with dynamical critical exponent z=2, and suggests a Bose-Einstein condensate interpretation.

Contribution

It introduces a nonrelativistic quantum membrane model with Lifshitz matter and gravity at z=2, connecting membrane ground states to string partition functions in a novel framework.

Findings

Constructed a z=2 Lifshitz gravity theory in D+1 dimensions.

Demonstrated the membrane ground state reproduces string partition functions.

Proposed a Bose-Einstein condensate interpretation of the string vacuum.

Abstract

We propose a quantum theory of membranes designed such that the ground-state wavefunction of the membrane with compact spatial topology \Sigma_h reproduces the partition function of the bosonic string on worldsheet \Sigma_h. The construction involves worldvolume matter at quantum criticality, described in the simplest case by Lifshitz scalars with dynamical critical exponent z=2. This matter system must be coupled to a novel theory of worldvolume gravity, also exhibiting quantum criticality with z=2. We first construct such a nonrelativistic "gravity at a Lifshitz point" with z=2 in D+1 spacetime dimensions, and then specialize to the critical case of D=2 suitable for the membrane worldvolume. We also show that in the second-quantized framework, the string partition function is reproduced if the spacetime ground state takes the form of a Bose-Einstein condensate of membranes in their first-quantized ground states, correlated across all genera.