Strings onAdS₂and the high-energy limit of noncritical M-theory

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 ′ → ∞ limit of string theory. In the related case of two-dimensional Type 0A strings, it has been argued that the conformal α ′ → ∞ 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 × 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 × 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."

Higher-spin Chern–Simons theories in odd dimensions

“…As the latter should cover in particular the infinite towers of massive HS states described by 10-dimensional string theory, it is very tempting to conjecture that osp(1|32) has to be enhanced to a HS extension, thus giving rise to Chern-Simons actions of the type considered here. In fact, recently it has been argued that the threedimensional Chern-Simons theory based on a HS algebra is related to M-theory for noncritical strings in D = 2 via the background AdS 2 × S 1 [62]. Similarly to the AdS 4 × S 1 solution discussed for the D = 5 theory here, one might hope to identify a non-topological 10-dimensional phase, which permits flat Minkowski space and gives rise to massive HS states via spontaneous symmetry breaking.…”

Two-dimensional black holes in a higher derivative gravity and matrix model

“…Furthermore, the curvature radius of the black hole solution is the order of string length scale, independent of charge, and therefore the low energy gravity can not be trusted and it is not clear whether the black hole exists at all. Nevertheless, there are some pursuits of matching between the matrix model and type 0A strings on black holes or AdS space [4][5] [6] with partial success.…”

Swampland Conjectures for an Almost Topological Gravity Theory

“…Clearly, for making progress we need a concrete and well treatable starting ground. For our purposes, this is provided by the non-critical M-theory in 3D proposed by Hořava/Keeler [9][10][11] which is exactly solvable in terms of a non-relativistic Fermi liquid in 2 +1 dimensions. This is motivated by the known tachyon condensation from ten-dimensional type 0 theories, which represent the infinite temperature limit of type II theories, to the two-dimensional type 0 theories [8].…”

“…This is motivated by the known tachyon condensation from ten-dimensional type 0 theories, which represent the infinite temperature limit of type II theories, to the two-dimensional type 0 theories [8]. The non-critical M-theory arises from the thermal version of this twodimensional theory when D0-branes are included [9][10][11]. In the conformal limit this theory was suggested to be described by an effective higher spin generalization of conformal gravity equipped with a higher spin matter field.…”