Membranes at Quantum Criticality
Dec, 2008Citations per year
Abstract: (arXiv)
We propose a quantum theory of membranes designed such that the ground-state wavefunction of the membrane with compact spatial topology \Sigma_h reproduces the partition function of the bosonic string on worldsheet \Sigma_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.- membrane: condensation
- ground state: wave function
- condensation: Bose-Einstein
- dimension: 2
- dimension: 3
- string model: boson
- partition function
- critical phenomena
- quantization
- Fock space
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