Nonrelativistic conformal field theories

Abstract

We study representations of the Schrödinger algebra in terms of operators in nonrelativistic conformal field theories. We prove a correspondence between primary operators and eigenstates of few-body systems in a harmonic potential. Using the correspondence we compute analytically the energy of fermions at unitarity in a harmonic potential near two and four spatial dimensions. We also compute the energy of anyons in a harmonic potential near the bosonic and fermionic limits.

26 pages, 9 figures; added a comment on the convergence of epsilon expansions

References in corpus (13)

• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• The unitary gas in an isotropic harmonic trap: symmetry properties and applications
• Epsilon expansion for a Fermi gas at infinite scattering length
• Renormalization group fixed points, universal phase diagram, and 1/N expansion for quantum liquids with interactions near the unitarity limit
• Vanishing bulk viscosities and conformal invariance of unitary Fermi gas
• Conformal Invariance for Non-Relativistic Field Theory
• Aharonov-Bohm Scattering, Contact Interactions and Scale Invariance
• Fermi gas near unitarity around four and two spatial dimensions
• Unitary Fermi Gas in a Harmonic Trap
• BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
• Schroedinger Self-adjoint Extension and Quantum Field Theory
• Finite and Infinite Symmetries in (2+1)-Dimensional Field Theory
• Short Range Scaling Laws of Quantum Gases With Contact Interactions

Cited by in corpus (257)

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• Non-relativistic holography
• Conformality Lost
• Galilean Conformal Algebras and AdS/CFT
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• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• GCA in 2d
• On String Theory Duals of Lifshitz-like Fixed Points
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• Tan relations in one dimension
• Holographic stress tensor for non-relativistic theories
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• Renormalization of Lorentz violating theories
• On instantons as Kaluza-Klein modes of M5-branes
• Field Theories with Conformal Carrollian Symmetry
• On Representations and Correlation Functions of Galilean Conformal Algebras
• Schroedinger Invariance from Lifshitz Isometries in Holography and Field Theory
• Conformal quantum mechanics as the CFT${}_1$ dual to AdS${}_2$
• Viscosity of strongly interacting quantum fluids: spectral functions and sum rules
• On the spectrum of nonrelativistic AdS/CFT
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• Quantum anomaly, universal relations, and breathing mode of a two-dimensional Fermi gas
• Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly-interacting Fermi Gas
• Superadiabatic quantum friction suppression in finite-time thermodynamics
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Correlation Functions in Non-Relativistic Holography
• Quantum criticality and black holes
• 1/N Effects in Non-Relativistic Gauge-Gravity Duality
• AdS/CFT duality for non-relativistic field theory
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• Selected Topics in the Large Quantum Number Expansion
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• Supersymmetric IIB Solutions with Schrödinger Symmetry
• Heavy Operators and Hydrodynamic Tails
• Fluid Dynamics and Viscosity in Strongly Correlated Fluids
• Lattice methods for strongly interacting many-body systems
• Galilean Superconformal Symmetries
• When Superconductivity Crosses Over: From BCS to BEC
• Lattice Monte Carlo calculations for unitary fermions in a finite box
• Correlation functions in the non-relativistic AdS/CFT correspondence
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• Supersymmetric Extension of Galilean Conformal Algebras
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• Lattice Monte Carlo calculations for unitary fermions in a harmonic trap
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• Shortcuts to adiabaticity in the strongly-coupled regime: nonadiabatic control of a unitary Fermi gas
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• Renormalization in the Three-body Problem with Resonant P-wave Interactions
• Intertwining Operator Realization of Non-Relativistic Holography
• Hilbert Series and Operator Basis for NRQED and NRQCD/HQET
• Geometry of Schroedinger Space-Times, Global Coordinates, and Harmonic Trapping
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• Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs
• Liberating Efimov physics from three dimensions
• Super Galilean conformal algebra in AdS/CFT
• Shear Viscosity of a Unitary Fermi Gas
• Remark on quantum mechanics with conformal Galilean symmetry
• Non-relativistic CFT and Semi-classical Strings
• Finite-temperature equation of state of polarized fermions at unitarity
• Super Schrodinger algebra in AdS/CFT
• The Exact Renormalization Group and Higher-spin Holography
• Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
• Unitary Fermi gas, epsilon expansion, and nonrelativistic conformal field theories
• Exotic symmetry and monodromy equivalence in Schrodinger sigma models
• On the convergence of nuclear effective field theory with perturbative pions
• Fluctuating relativistic dissipative hydrodynamics as a gauge theory
• Universal Two-body Physics in Dark Matter near an S-wave Resonance
• Universal four-component Fermi gas in one dimension
• Galilean Conformal Algebra in Two Dimensions and Cosmological Topologically Massive Gravity
• Universal phase diagram and scaling functions of imbalanced Fermi gases
• Entanglement negativity in Galilean conformal field theories
• OPE convergence in non-relativistic conformal field theories
• Probing strongly interacting atomic gases with energetic atoms
• Unnuclear physics
• Anisotropic gravity solutions in AdS/CMT
• Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence
• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• Towards a gravity dual of the unitary Fermi gas
• Lectures on Conformal Field Theory
• Aspects of Non-Relativistic Quantum Field Theories
• On a scale-invariant Fermi gas in a time-dependent harmonic potential
• Renormalization of Galilean Electrodynamics
• A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities
• Very Special Conformal Field Theories (VSCFT) and their holographic duals
• Asymptotic symmetries of Schrödinger spacetimes
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• Viscosity Sum Rules at Large Scattering Lengths
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• The Non-Relativistic Superparticle in a Curved Background
• Quantum Many-Body Conformal Dynamics: Symmetries, Geometry, Conformal Tower States, and Entropy Production
• Quantum critical thermal transport in the unitary Fermi gas
• Solitons as Probes of the Structure of Holographic Superfluids
• Holographic Flavor Transport in Schroedinger Spacetime
• Non-conformal Hydrodynamics in Einstein-dilaton Theory
• Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics
• Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes
• Observables and Correlators in Nonrelativistic ABJM Theory
• A family of super Schrodinger invariant Chern-Simons matter systems
• The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
• Transport in non-conformal holographic fluids
• The Shadow Formalism of Galilean CFT${}_2$
• Existence and Construction of Galilean invariant $z\ne 2$ Theories
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• Universal dimer-dimer scattering in lattice effective field theory
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• Particle Number and 3D Schroedinger Holography
• Establishing Conservation Laws in Pair Correlated Many Body theories: T matrix Approaches
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• The Role of the Effective Range in Resonantly Interacting Fermi Gases: How Breaking Scale Symmetry Affects the Bulk Viscosity
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• Observation of Dynamical Super Efimovian Expansion in a Unitary Fermi Gas
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• From AdS to Schrödinger/Lifshitz dual space-times without or with hyperscaling violation
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• Supersymmetric Galilean Electrodynamics
• Schrodinger Holography for z<2
• Far-Away-From-Equilibrium Quantum Critical Conformal Dynamics: Reversibility, Thermalization, and Hydrodynamics
• General Freeze-in and Freeze-out
• Renormalization group analysis of resonantly interacting anyons
• Dynamics of strongly interacting Fermi gases with time-dependent interactions: Consequence of conformal symmetry
• Flat Bands and Compact Localised States: A Carrollian roadmap
• Ideal gas matching for thermal Galilean holography
• Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases
• More on the operator-state map in non-relativistic CFTs
• Conformal Structure of the Heavy Particle EFT Operator Basis
• The entanglement spectrum and Rényi entropies of non-relativistic conformal fermions
• Fate of Multiparticle Resonances: From $Q$-Balls to ${}^3$He Droplets
• Holographic Entanglement negativity in flat space generalized minimal massive gravity
• Schrodinger Fermi Liquids
• Galilean conformal algebras in two spatial dimension
• Shear viscosity and spin sum rules in strongly interacting Fermi gases
• Hydrodynamic Attractor in Ultracold Atoms
• Transdimensional equivalence of universal constants for Fermi gases at unitarity
• Exponential nonlinear electrodynamics and backreaction effects on Holographic superconductor in the Lifshitz black hole background
• Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space
• Conformal Quantum Mechanics, Holomorphic Factorisation, and Ultra-Spinning Black Holes
• Effective Lagrangian of unitary Fermi gas from $\epsilon$ expansion
• Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions
• Efimov effect at the Kardar-Parisi-Zhang roughening transition
• Triviality of Entanglement Entropy in the Galilean Vacuum
• Fidelity susceptibility for Lifshitz geometries via Lifshitz Holography
• Complex scaling flows in the quench dynamics of interacting particles
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
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• Towards a Non-Relativistic Holographic Superfluid
• The Conformal Spectrum of Non-Abelian Anyons
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• How to Build a Black Hole out of Instantons
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• Instantons, Integrability and Discrete Light-Cone Quantisation
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• Universal scaling of work statistics for quantum quenches
• Solitonic Phase Transitions of Galilean Black Holes
• Bulk viscosity of resonantly interacting fermions in the quantum virial expansion
• Energy loss and jet quenching parameter in a thermal non-relativistic, non-commutative Yang-Mills plasma
• Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
• The fate of conformal symmetry in the non-linear Schrödinger theory
• Effective field theory for one-dimensional nonrelativistic particles with contact interaction
• Non-relativistic Conformal Field Theory in the Presence of Boundary
• Asymptotically Schrödinger Space-Times
• Teleparallel formalism of galilean gravity
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Dynamical violation of scale invariance and the dilaton in a cold Fermi gas
• Three-body contact for fermions. I. General relations
• Multi-graded Galilean conformal algebras
• Numerical study of unitary fermions in one spatial dimension
• Carroll-Schrödinger Equation
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Lattice methods and effective field theory
• Scale Invariance in the Lowest Landau Level
• Revisiting Wilson loops for nonrelativistic backgrounds
• A New Theory of Anyons
• Generalized Massive Gravity and Galilean Conformal Algebra in two dimensions
• About the Non Relativistic Structure of the AdS/CFT Superalgebras
• Conformal Galilean Spin-3 Gravity in 3d
• Towards a Gravity Dual for the Large Scale Structure of the Universe
• Quantum anomaly and thermodynamics of one-dimensional fermions with antisymmetric two-body interactions
• Weyl Anomaly in NonRelativistic CFTs
• Entanglement Negativity in Flat Holography
• On non-relativistic $Q\bar{Q}$ potential via Wilson loop in Galilean space-time
• Schrödinger Holography with $z=2$
• Higher spin holography with Galilean symmetry in general dimensions
• Reflections on dipolar quantum fluids
• Scale and conformal invariance in rotating interacting few-fermion systems
• Quantum-critical electrodynamics of Luttinger fermions
• Hydrodynamic attractor in periodically driven ultracold quantum gases
• Quantum $z=2$ Lifshitz criticality in one-dimensional interacting fermions
• Gravity Dual for Very Special Conformal Field Theories in type IIB Supergravity
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• Massive Nambu-Goldstone Fermions and Bosons for Non-relativistic Superconformal Symmetry: Jackiw-Pi Vortices in a Trap
• Exact evaluation of large-charge correlation functions in non-relativistic conformal field theory
• Dilaton in a cold Fermi gas
• Spatially Random Disorder in Unitary Fermion System in $(4-\epsilon )$-Dimensions and Effective Action at Finite Temperature
• Note About Hamiltonian Dynamics of String in Non-Relativistic D3-Brane Background
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• Penrose Limit and Non-relativistic geometries
• Universal Properties of Weakly Bound Two-Neutron Halo Nuclei
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Effective field theory for weakly bound two-neutron halo nuclei: corrections from neutron-neutron effective range
• Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance
• Model-independent mass determination of near-threshold states from short-range production
• Developments in non-relativistic field theory and complexity
• Pseudo-mass parameterized alchemical equation: a generalisation of the molecular Schrödinger equation
• Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure
• Short-distance production of three particles with large scattering length
• UV/IR symmetries of the $S$-matrix and RG flow
• Heisenberg Symmetry and Collective Modes of One Dimensional Unitary Correlated Fermions
• Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry