Relativistic gravity and parity-violating nonrelativistic effective field theories

We show that the relativistic gravity theory can offer a framework to formulate the nonrelativistic effective field theory in a general coordinate invariant way. We focus on the parity violating case in 2 + 1 dimensions which is particularly appropriate for the study on quantum Hall effects and chir...

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Bibliographic Details
Published in:Physical review. D, Particles, fields, gravitation, and cosmology Particles, fields, gravitation, and cosmology, 2015-06, Vol.91 (12), Article 126004
Main Authors: Wu, Chaolun, Wu, Shao-Feng
Format: Article
Language:English
Subjects:
Density
Field theory
Fluids
Gages
Gravitation
Invariants
Low energy
Magnetic fields
Orbitals
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Summary:We show that the relativistic gravity theory can offer a framework to formulate the nonrelativistic effective field theory in a general coordinate invariant way. We focus on the parity violating case in 2 + 1 dimensions which is particularly appropriate for the study on quantum Hall effects and chiral superfluids. We discuss how the nonrelativistic spacetime structure emerges from relativistic gravity. We present covariant maps and constraints that relate the field contents in the two theories, which also serve as the holographic dictionary in the context of gauge/gravity duality. A low energy effective action for fractional quantum Hall states is constructed, which captures universal geometric properties and generates nonuniversal corrections systematically. We give another holographic example with dyonic black brane background to calculate thermodynamic and transport properties of strongly coupled nonrelativistic fluids in magnetic field. In particular, by identifying the shift function in the gravity as a minus of guiding center velocity, we obtain the Hall viscosity with its relation to Landau orbital angular momentum density proportional to Wen-Zee shift. Our formalism has a good projection to lowest Landau level.
ISSN:1550-7998
1550-2368
DOI:10.1103/PhysRevD.91.126004