Strings on AdS_2 and the High-Energy Limit of Noncritical M-Theory

TL;DR

This paper explores the high-energy limit of noncritical M-theory in 2+1 dimensions, revealing an AdS_2×S^1 spacetime with a massless fermion, and proposes a topological higher-spin gravity description coupled to a Dirac field.

Contribution

It demonstrates that the high-energy limit of noncritical M-theory naturally leads to an AdS_2×S^1 background and introduces a topological higher-spin gravity framework coupled to a massless fermion.

Findings

High-energy limit yields AdS_2×S^1 spacetime.

The effective theory involves topological higher-spin gravity.

The original fermionic plane is twistor space related to the spacetime symmetry.

Abstract

Noncritical M-theory in 2+1 dimensions has been defined as a double-scaling limit of a nonrelativistic Fermi liquid on a flat two-dimensional plane. Here we study this noncritical M-theory in the limit of high energies, analogous to the \alpha'\to\infty limit of string theory. In the related case of two-dimensional Type 0A strings, it has been argued that the conformal \alpha'\to\infty limit leads to AdS_2 with a propagating fermion whose mass is set by the value of the RR flux. Here we provide evidence that in the high-energy limit, the natural ground state of noncritical M-theory similarly describes the AdS_2\times S^1 spacetime, with a massless propagating fermion. We argue that the spacetime effective theory in this background is captured by a topological higher-spin extension of conformal Chern-Simons gravity in 2+1 dimensions, consistently coupled to a massless Dirac field. Intriguingly, the two-dimensional plane populated by the original nonrelativistic fermions is essentially the twistor space associated with the symmetry group of the AdS_2\times S^1 spacetime; thus, at least in the high-energy limit, noncritical M-theory can be nonperturbatively described as a "Fermi liquid on twistor space."