Conformal Invariance for Non-Relativistic Field Theory

Abstract

Momentum space Ward identities are derived for the amputated n-point Green's functions in 3+1 dimensional non-relativistic conformal field theory. For n=4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Green's functions) are considered. Any scale invariant 2-to-2 scattering amplitude is also conformally invariant. However, conformal invariance imposes constraints on off-shell Green's functions and the three particle scattering amplitude which are not automatically satisfied if they are scale invariant. As an explicit example of a conformally invariant theory we consider non-relativistic particles in the infinite scattering length limit.

12 pages, journal version, additional clarifying remarks added

Cited by in corpus (96)

• Universality in Few-body Systems with Large Scattering Length
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Effective Field Theory for Few-Nucleon Systems
• Nuclear effective field theory: status and perspectives
• Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Nonrelativistic conformal field theories
• Implications of conformal invariance in momentum space
• Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality
• Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
• Schr"odinger invariance and space-time symmetries
• Holographic stress tensor for non-relativistic theories
• Renormalization of Lorentz violating theories
• The Dilute Bose-Einstein Condensate with Large Scattering Length
• alpha-alpha Scattering in Halo Effective Field Theory
• 1/N Effects in Non-Relativistic Gauge-Gravity Duality
• AdS/CFT duality for non-relativistic field theory
• Conformal non-relativistic hydrodynamics from gravity
• Supersymmetric IIB Solutions with Schrödinger Symmetry
• Lattice methods for strongly interacting many-body systems
• Symmetry from Entanglement Suppression
• Black holes and non-relativistic quantum systems
• Minimal Entanglement and Emergent Symmetries in Low-energy QCD
• Non-Relativistic M2-brane Gauge Theory and New Superconformal Algebra
• A renormalized equation for the three-body system with short-range interactions
• Bulk Viscosity of a Gas of Massless Pions
• Anisotropic scaling and generalized conformal invariance at Lifshitz points
• An effective field theory for coupled-channel scattering
• Induced p-wave superfluidity in two dimensions: Brane world in cold atoms and nonrelativistic defect CFTs
• Super Galilean conformal algebra in AdS/CFT
• Finite-temperature equation of state of polarized fermions at unitarity
• The particle number in Galilean holography
• Super Schrodinger algebra in AdS/CFT
• Lifshitz Field Theories at Non-Zero Temperature, Hydrodynamics and Gravity
• Geometry and entanglement in the scattering matrix
• Operator Product Expansion and Conservation Laws in Non-Relativistic Conformal Field Theories
• Naturalness in Nuclear Effective Field Theories
• OPE convergence in non-relativistic conformal field theories
• Unnuclear physics
• Towards a gravity dual of the unitary Fermi gas
• Nonrelativistic Conformal Field Theories in the Large Charge Sector
• Renormalization of Galilean Electrodynamics
• Wilsonian RG and Redundant Operators in Nonrelativistic Effective Field Theory
• The Spinful Large Charge Sector of Non-Relativistic CFTs: From Phonons to Vortex Crystals
• On Non-Relativistic Conformal Field Theory and Trapped Atoms: Virial Theorems and the State-Operator Correspondence in Three Dimensions
• Non-Relativistic Holography -- A Group-Theoretical Perspective
• Viscosity Sum Rules at Large Scattering Lengths
• Charge-Hyperscaling Violating Lifshitz hydrodynamics from black-holes
• Ground-state energy of the unitary Fermi gas from the epsilon expansion
• Holographic Flavor Transport in Schroedinger Spacetime
• A family of super Schrodinger invariant Chern-Simons matter systems
• Symmetries and currents of the ideal and unitary Fermi gases
• Hyperscaling-Violating Lifshitz hydrodynamics from black-holes: Part II
• Hints of Entanglement Suppression in Hyperon-Nucleon Scattering
• Existence and Construction of Galilean invariant $z\ne 2$ Theories
• Drag force in a hot non-relativistic, non-commutative Yang-Mills plasma
• Renormalization properties of a Galilean Wess-Zumino model
• Conformal symmetry and non-relativistic second order fluid dynamics
• Galilean anti-de-Sitter spacetime in Romans theory
• Effective theory for the Goldstone field in the BCS-BEC crossover at T=0
• Particle Number and 3D Schroedinger Holography
• Charged, conformal non-relativistic hydrodynamics
• Bulk viscosity of resonating fermions revisited: Kubo formula, sum rule, and the dimer and high-temperature limits
• Unitarity and Universality in non relativistic Conformal Field theory
• Structure Function Sum rules for Systems with Large Scattering Lengths
• From AdS to Schrödinger/Lifshitz dual space-times without or with hyperscaling violation
• Conformal Structure of the Heavy Particle EFT Operator Basis
• Entanglement suppression and low-energy scattering of heavy mesons
• Ideal gas matching for thermal Galilean holography
• Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases
• Schrodinger Fermi Liquids
• Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space
• Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions
• Efimov effect at the Kardar-Parisi-Zhang roughening transition
• Towards a Non-Relativistic Holographic Superfluid
• Open String in Non-Relativistic Background
• D2-D8 system with massive strings and the Lifshitz spacetimes
• Galilean type IIA backgrounds and a map
• Microscopic derivation of the Boltzmann equation for transport coefficients of resonating fermions at high temperature
• Lowest weight representations of super Schrodinger algebras in low dimensional spacetime
• Applied nonrelativistic conformal field theory: scattering-length and effective-range corrections to unnuclear physics
• From Nuclear to Unnuclear Physics
• Supersymmetry of the Schrodinger and PP Wave Solutions in Einstein-Weyl Supergravities
• Bulk viscosity of resonantly interacting fermions in the quantum virial expansion
• Non-relativistic Conformal Field Theory in the Presence of Boundary
• Gauss-Bonnet black holes in a special anisotropic scaling spacetime
• Weyl Anomaly in NonRelativistic CFTs
• RG flows and cascades of $Li{f}_4^{(2)}\times S^1\times S^5$ vacua
• Scale and conformal invariance in rotating interacting few-fermion systems
• 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
• Exact evaluation of large-charge correlation functions in non-relativistic conformal field theory
• Model-independent mass determination of near-threshold states from short-range production
• UV/IR symmetries of the $S$-matrix and RG flow
• Symmetries of the nucleon-nucleon $S$-matrix and effective field theory expansions