Relativistic Gravity and Parity-Violating Non-Relativistic Effective Field Theories
arXiv:1409.8265 · doi:10.1103/PhysRevD.91.126004
Abstract
We show that the relativistic gravity theory can offer a framework to formulate the non-relativistic 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 non-relativistic 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 context of gauge/gravity duality. A low energy effective action for fractional quantum Hall states is constructed, which captures universal geometric properties and generates non-universal corrections systematically. We give another holographic example with dyonic black brane background to calculate thermodynamic and transport properties of strongly coupled non-relativistic fluids in magnetic field. In particular, by identifying the shift function in the gravity as 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.
arXiv comment6 pages
References in corpus (42)
- Large N Field Theories, String Theory and Gravity
- Quantum Gravity at a Lifshitz Point
- Gravity Duals of Lifshitz-like Fixed Points
- Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
- Gravity duals for non-relativistic CFTs
- Membranes at Quantum Criticality
- Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
- Viscosity of Quantum Hall Fluids
- General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
- Hall Viscosity and Electromagnetic Response
- Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
- Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
- Hall conductivity from dyonic black holes
- Black holes in Einstein-aether and Horava-Lifshitz gravity
- Torsional Newton-Cartan Geometry and Lifshitz Holography
- Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
- Spacetime Symmetries of the Quantum Hall Effect
- Black Holes in Einstein-Aether Theory
- Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
- Scaling in Plateau-to-Plateau Transition: A Direct Connection of Quantum Hall Systems with Anderson Localization Model
- Thermal Hall Effect and Geometry with Torsion
- Parity-Violating Hydrodynamics in 2+1 Dimensions
- Density-curvature response and gravitational anomaly
- General Covariance in Gravity at a Lifshitz Point
- Non-relativistic holography from Horava gravity
- Geometry of Fractional Quantum Hall Fluids
- Lifshitz holography: The whole shebang
- Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
- A new formulation of non-relativistic diffeomorphism invariance
- Effective theory of chiral two-dimensional superfluids
- String theory embeddings of non-relativistic field theories and their holographic Horava gravity duals
- General coordinate invariance in quantum many-body systems
- Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation
- On Nonrelativistic Diffeomorphism Invariance
- Effective Field Theory of Relativistic Quantum Hall Systems
- Generalized dilatation operator method for non-relativistic holography
- The Euler current and relativistic parity odd transport
- More On Nonrelativistic Diffeomorphism Invariance
- Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
- Charged black holes in Horava gravity
- Asymptotically hyperbolic black holes in Horava gravity
- Thermal Transport in a Noncommutative Hydrodynamics