2014/10/31 by Frank D. Ferrari, Frank Ferrari, Semyon Klevtsov
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Classical mechanics #Computation #Cosmology and Gravitation Theories #Curvature #Field (mathematics) #Field theory (psychology) #Free field #Geometry #Geometry and complex manifolds #Gravitation #Mathematical physics #Mathematics #Path integral formulation #Physics #Pure mathematics #Quantum #Quantum mechanics #Remainder #Representation (politics) #Scalar (mathematics) #Scalar curvature #Theoretical physics #Transformation (genetics) #cond-mat.str-el #hep-th #math.DG
paper · pdf · doi:10.1007/jhep12(2014)086
published as JHEP12(2014)086 · 14 pages; v3: conformal spin rescaled, minor changes
openalex publication_date 2014/12/01 · arxiv created 2014/12/13 · arxiv updated 2014/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.