Thermodynamics of noncritical M-theory and the topological A-model

Self Cite

694

1,031

We propose a quantum theory of membranes designed such that the ground-state wavefunction of the membrane with compact spatial topology Σ h reproduces the partition function of the bosonic string on worldsheet Σ 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.

Section: Discussionmentioning

confidence: 99%

Section: Worldvolume Matter: Lifshitz Scalars and Quantum Criticalitymentioning

confidence: 99%

Membranes at quantum criticality

Hořava¹

2009

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694

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“…This hierarchy is based on shifts of both the energy and angular momentum quantum numbers of the single-fermion Hilbert space of the dual 0A matrix model description. The utilization of the fermion angular momentum as a dynamical variable is reminiscent of the proposed non-critical M-theory [24,25] perspective on 0A string theory, although we introduce it for purely mathematical ends. The complex nature of the integrable structure provides an additional real constraint (string equation) on the operator algebra of the theory, relative to previous integrability analyses.…”

Section: Jhep12(2006)008mentioning

confidence: 99%

“…The holomorphic perturbations above are less clearly interpreted, and perhaps should be understood as generating coherent states of D-branes or discrete states. Alternatively, the interpretation may lie outside of 0A string theory itself and require ideas from non-critical M-theory [24,25]. It would be of great interest to understand the full physical interpretation of these perturbations and the complex Toda structure introduced herein.…”

Section: Jhep12(2006)008mentioning

confidence: 99%

Integrable deformations of hat c = 1 strings in flux backgrounds

Davis

Larsen

O’Connell

et al. 2006

We study d = 2 0A string theory perturbed by tachyon momentum modes in backgrounds with non-trivial tachyon condensate and Ramond-Ramond (RR) flux. In the matrix model description, we uncover a complexified Toda lattice hierarchy constrained by a pair of novel holomorphic string equations. We solve these constraints in the classical limit for general RR flux and tachyon condensate. Due to the non-holomorphic nature of the tachyon perturbations, the transcendental equations which we derive for the string susceptibility are manifestly non-holomorphic. We explore the phase structure and critical behavior of the theory.

“…In the full critical string case, we know very little about full M-theory beyond the use of either nonperturbative dualities, or the low-energy limit as described by elevendimensional supergravity. Following the resurgence of interest in two-dimensional Type 0A and 0B string theories [6][7][8], in [9,10] we proposed a nonperturbative definition of noncritical M-theory in 2 + 1 dimensions, related to Type 0A and 0B strings in two dimensions by a string/M-theory duality. The definition of noncritical M-theory as given in [9] is in terms of a double-scaling limit of a nonrelativistic Fermi liquid on a rigid two-dimensional plane.…”

Section: Introductionmentioning

confidence: 99%

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

Hořava

Keeler

2007

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."