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.

14 pages; v3: conformal spin rescaled, minor changes

References in corpus (9)

• Spacetime Symmetries of the Quantum Hall Effect
• 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
• Thermal Hall Effect and Geometry with Torsion
• Density-curvature response and gravitational anomaly
• Hall viscosity, topological states and effective theories
• FQHE on curved backgrounds, free fields and large N
• Matrix models and growth processes: from viscous flows to the quantum Hall effect
• Ward Identities for Hall Transport

Cited by in corpus (12)

• Topological central charge from Berry curvature: gravitational anomalies in trial wavefunctions for topological phases
• FQHE on curved backgrounds, free fields and large N
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Microscopic Model for Fractional Quantum Hall Nematics
• Anisotropic Quantum Hall Droplets
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Quantum Hall States and Conformal Field Theory on a Singular Surface
• Geometry and large N limits in Laughlin states
• Gravitational action for a massive Majorana fermion in 2d quantum gravity
• Geometric and computational aspects of chiral topological quantum matter
• Adiabatic Deformations of Quantum Hall Droplets
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect