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

TL;DR

This paper analyzes the high-energy ($\alpha'\to\infty$) limit of noncritical M-theory in 2+1 dimensions, arguing that the natural ground state describes an $AdS_2\times S^1$ spacetime with a massless Dirac fermion. The spacetime dynamics are captured by a topological higher-spin extension of conformal gravity in 2+1 dimensions, consistently coupled to the fermion, with the planar Fermi-liquid interpreted as twistor space for the $SO(3,2)$ symmetry. The construction combines an $SO(3,2)$ Chern-Simons gravity description, a higher-spin extension ${\cal W}_0$, and an unfolded-matter coupling à la Vasiliev, providing a concrete dual-like framework for this noncritical M-theory limit. The results illuminate how an ostensibly nonrelativistic Fermi system encodes relativistic AdS holography and hint at deeper links between high-energy limits of string/M-theory, higher-spin gauge theories, and twistor-theoretic descriptions.

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 α'\to\infty limit of string theory. In the related case of two-dimensional Type 0A strings, it has been argued that the conformal α'\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."