Noncritical M-Theory in 2+1 Dimensions as a Nonrelativistic Fermi Liquid

TL;DR

This paper proposes a noncritical M-theory in 2+1 dimensions modeled as a nonrelativistic Fermi liquid, connecting 2D string theories, and explores its vacuum structure, dualities, and emergent spacetime features.

Contribution

It introduces a novel noncritical M-theory framework using a double-scaled Fermi liquid, linking string theories and revealing emergent spacetime and duality properties.

Findings

Exact vacuum energy calculation suggests a duality with the Debye phonon model.

Identification of solutions describing decay between different 2D string theories.

Emergent spacetime only for states with hydrodynamic descriptions.

Abstract

We claim that the dynamics of noncritical string theories in two dimensions is related to an underlying noncritical version of M-theory, which we define in terms of a double-scaled nonrelativistic Fermi liquid in 2+1 dimensions. After reproducing Type 0A and 0B string theories as solutions, we study the natural M-theory vacuum. The vacuum energy of this solution can be evaluated exactly, its form suggesting a duality to the Debye model of phonons in a melting solid, and a possible topological nature of the theory. The physical spacetime is emergent in this theory, only for states that admit a hydrodynamic description. Among the solutions of the hydrodynamic equations of motion for the Fermi surface, we find families describing the decay of one two-dimensional string theory into another via an intermediate M-theory phase.