FQHE on curved backgrounds, free fields and large N

Abstract

We study the free energy of the Laughlin state on curved backgrounds, starting from the free field representation. A simple argument, based on the computation of the gravitational effective action from the transformation properties of Green functions under the change of the metric, allows to compute the first three terms of the expansion in large magnetic field. The leading and subleading contributions are given by the Aubin-Yau and Mabuchi functionals respectively, whereas the Liouville action appears at next-to-next-to-leading order. We also derive a path integral representation for the remainder terms. They correspond to a large mass expansion for a related interacting scalar field theory and are thus given by local polynomials in curvature invariants.

arXiv comment14 pages; v3: conformal spin rescaled, minor changes

References in corpus (24)

• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Viscosity of Quantum Hall Fluids
• Hall Viscosity and Electromagnetic Response
• Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
• Quantum Hall Effect in Higher Dimensions
• Spacetime Symmetries of the Quantum Hall Effect
• Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
• Thermal Hall Effect and Geometry with Torsion
• Density-curvature response and gravitational anomaly
• Newton-Cartan Geometry and the Quantum Hall Effect
• Bergman Kernel from Path Integral
• Hall viscosity, topological states and effective theories
• Quantum mechanics and quantum Hall effect on Riemann surfaces
• FQHE on curved backgrounds, free fields and large N
• Gravitational Actions in Two Dimensions and the Mabuchi Functional
• Random normal matrices, Bergman kernel and projective embeddings
• Kahler-Einstein metrics emerging from free fermions and statistical mechanics
• Anomalous Hydrodynamics of Fractional Quantum Hall States
• Matrix models and growth processes: from viscous flows to the quantum Hall effect
• Ward Identities for Hall Transport
• On the Lower Order Terms of the Asymptotic Expansion of Zelditch

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• Bimetric Theory of Fractional Quantum Hall States
• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• Boundary effective action for quantum Hall states
• Geometry of Quantum Hall States: Gravitational Anomaly and Kinetic Coefficients
• Geometric adiabatic transport in quantum Hall states
• Quantum Hall effect and Quillen metric
• FQHE on curved backgrounds, free fields and large N
• Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
• Investigating anisotropic quantum Hall states with bi-metric geometry
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Collective Field Theory for Quantum Hall States
• Probing topological superconductors with emergent gravity
• Particle-Hole Duality in the Lowest Landau Level
• Geometric Defects in Quantum Hall States
• Multipole Expansion in the Quantum Hall Effect
• Microscopic Model for Fractional Quantum Hall Nematics
• Boundary central charge from bulk odd viscosity - chiral superfluids
• The boundary density profile of a Coulomb droplet. Freezing at the edge
• Collective excitations at filling factor 5/2: The view from superspace
• Lowest Landau level on a cone and zeta determinants
• On the full asymptotic of analytic torsion
• Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
• Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states
• Geometric responses of the Pfaffian state
• Anisotropic Quantum Hall Droplets
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• Laughlin states on higher genus Riemann surfaces
• Vortex flows on closed surfaces
• Hall Viscosity in the Non-Abelian Quantum Hall Matrix Model
• Mabuchi spectrum from the minisuperspace
• Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
• Quantum Hall States and Conformal Field Theory on a Singular Surface
• 2D gravitational Mabuchi action on Riemann surfaces with boundaries
• BRST cohomology of timelike Liouville theory
• Central charge from adiabatic transport of cusp singularities in the quantum Hall effect
• Minisuperspace computation of the Mabuchi spectrum
• Geometry and large N limits in Laughlin states
• Gravitational action for a massive Majorana fermion in 2d quantum gravity
• Adiabatic Deformations of Quantum Hall Droplets
• Geometric and computational aspects of chiral topological quantum matter
• Liouville perturbation theory for Laughlin state and Coulomb gas
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
• Laughlin states change under large geometry deformations and imaginary time Hamiltonian dynamics
• Bergman kernel asymptotics for singular metrics on punctured Riemann surfaces