2d Galilean Field Theories with Anisotropic Scaling

Abstract

In this work, we study two-dimensional Galilean field theories with global translations and anisotropic scaling symmetries. We show that such theories have enhanced local symmetries, generated by the infinite dimensional spin-l Galilean algebra with possible central extensions, under the assumption that the dilation operator is diagonalizable and has a discrete and non-negative spectrum. We study the Newton-Cartan geometry with anisotropic scaling, on which the field theories could be defined in a covariant way. With the well-defined Newton-Cartan geometry we establish the state-operator correspondence in anisotropic GCFT, determine the two-point functions of primary operators, and discuss the modular properties of the torus partition function which allows us to derive Cardy-like formulae.

arXiv comment39 pages; v2: 40 pages, note and references added, typos corrected; v3: reference added, typos corrected; v4: minor revision on section4 and section 7

References in corpus (66)

• Observation of resonance condensation of fermionic atom pairs
• Lectures on holographic methods for condensed matter physics
• Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
• Gravity Duals of Lifshitz-like Fixed Points
• The Kerr/CFT Correspondence
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Aspects of the BMS/CFT correspondence
• Chiral Gravity in Three Dimensions
• Warped AdS_3 Black Holes
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• The BMS/GCA correspondence
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Galilean Conformal Algebras and AdS/CFT
• A holographic reduction of Minkowski space-time
• Holography of 3d Flat Cosmological Horizons
• BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic Symmetries
• Newtonian Gravity and the Bargmann Algebra
• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
• Warped Conformal Field Theory
• GCA in 2d
• A spacetime derivation of the Lorentzian OPE inversion formula
• New Boundary Conditions for AdS3
• Non-relativistic conformal symmetries and Newton-Cartan structures
• Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity
• Chiral Scale and Conformal Invariance in 2D Quantum Field Theory
• On Representations and Correlation Functions of Galilean Conformal Algebras
• Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
• On the coupling of Galilean-invariant field theories to curved spacetime
• Warped Conformal Field Theory as Lower Spin Gravity
• Local scale invariance and strongly anisotropic equilibrium critical systems
• Newton-Cartan Geometry and the Quantum Hall Effect
• A tauberian theorem for the conformal bootstrap
• Entanglement Entropy in Warped Conformal Field Theories
• Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes
• Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes
• Modifications to Holographic Entanglement Entropy in Warped CFT
• 3D Flat Holography: Entropy and Logarithmic Corrections
• Comments on Galilean conformal field theories and their geometric realization
• Uplifting AdS3/CFT2 to Flat Space Holography
• The BMS Bootstrap
• A new formulation of non-relativistic diffeomorphism invariance
• Warped Weyl fermion partition functions
• Tweaking one-loop determinants in AdS${}_3$
• The nuts and bolts of the BMS Bootstrap
• A Crossing-Symmetric OPE Inversion Formula
• Correlation Functions of Warped CFT
• A note on the complex SYK model and warped CFTs
• Locality and anomalies in warped conformal field theory
• Bootstrapping holographic warped CFTs or: how I learned to stop worrying and tolerate negative norms
• Torsional Newton-Cartan geometry from Galilean gauge theory
• Anomalies for Galilean fields
• Entanglement and chaos in warped conformal field theories
• OPE convergence in non-relativistic conformal field theories
• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Scaling and conformal symmetries for plane gravitational waves
• Warped Black Holes in Lower-Spin Gravity
• Localisation of the Galilean symmetry and dynamical realisation of Newton-Cartan geometry
• Structure Constants from Modularity in Warped CFT
• Rényi Mutual Information in Holographic Warped CFTs
• On conjectured local generalizations of anisotropic scale invariance and their implications
• Possible Central Extensions of Non-Relativistic Conformal Algebras in 1+1
• From scale invariance to Lorentz symmetry
• Note on Bulk Reconstruction in AdS${}_3$/WCFT${}_2$

Cited by in corpus (13)

• The Holographic Nature of Null Infinity
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• On Higher-dimensional Carrollian and Galilean Conformal Field Theories
• A BMS-invariant free scalar model
• A BMS-invariant free fermion model
• On Galilean conformal bootstrap
• Supersymmetric Warped Conformal Field Theory
• Warped Flatland
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• Anisotropic conformal Carroll field theories and their gravity duals
• Thermal Corrections to Rényi Entropy in BMS Field Theory
• Universal sectors of two-dimensional Carrollian CFTs
• Anisotropic scaling non-relativistic holography: a symmetry perspective