Membranes at Quantum Criticality

By Petr Hořava. 2008

664 citations recorded by the source corpus.

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

Subfields: Biomedical Engineering, Electronic, Optical and Magnetic Materials, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/241220c4f696bba8e0e2bef2c28be25ed492e1b7

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Citations in the corpus

A dynamical inconsistency of Horava gravity (2009, background): “The restriction to six derivatives comes from the requirement of being power-counting renormalizable [1, 2].”
Strong coupling in Horava gravity (2009, background): “Hořava has recently proposed an interesting toy model of quantum gravity [1–3], generating a whole slew of publications that examine various aspects of the theory (see, for example [4–9]).”
Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography (2013, methodology): “This Lagrangian has striking similarities with Hořava–Lifshitz (HL) type Lagrangians [55].”
Horava-Lifshitz Cosmology (2009, background): “It has been argued in [5] that λ will eventually reach three possible IR fixed points: λ = 1, λ = 1/3 or λ = ∞.”
General covariance in quantum gravity at a Lifshitz point (2010, methodology): “Thus, the scalar dispersion relation degenerates to ω(2) = 0 in the limit of λ → 1 [1, 2].”
Relativistic Quantum Gravity at a Lifshitz Point (2009, background): “The innovative result of Hořava in [8, 9] was to realize that a Landau model for gravity, with critical exponent z = 3, could be written at the price of giving up the full diffeomorphisms invariance of GR.”
Structure formation in f(T) gravity and a solution for H0 tension (2018, background): “from its curvature formulation, and extend the Einstein-Hilbert action in various ways, for instance, the f(R) gravity [4], Gauss-Bonnet gravity [5], Lovelock gravity [6], Hořava-Lifshitz gravity [7], massive gravity [8] and several others.”