Holographic real-time non-relativistic correlators at zero and finite temperature

Abstract

We compute a variety of two and three-point real-time correlation functions for a strongly-coupled non-relativistic field theory. We focus on the theory conjectured to be dual to the Schrödinger-invariant gravitational spacetime introduced by Balasubramanian, McGreevy, and Son, but our methods apply to a large class of non-relativistic theories. At zero temperature, we obtain time-ordered, retarded, and Wightman non-relativistic correlators for scalar operators of arbitrary conformal dimension directly in field theory by applying a certain lightlike Fourier transform to relativistic conformal correlators, and we verify that non-relativistic AdS/CFT reproduces the results. We compute thermal two and three-point real-time correlators for scalar operators dual to scalar fields in the black hole background which is the finite temperature generalization of the Schrödinger spacetime. This is done by first identifying thermal real-time bulk-to-boundary propagators, which combined with Veltman's circling rules, yield two and three-point correlators. The two-point correlators we obtain satisfy the Kallen-Lehmann relations. We also give retarded and time-ordered three-point correlators.

55 pages; 5 appendices, 1 figure References added, PRD version

References in corpus (34)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Conformal collider physics: Energy and charge correlations
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Nonrelativistic conformal field theories
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Real-time gauge/gravity duality: Prescription, Renormalization and Examples
• Comments on string theory backgrounds with non-relativistic conformal symmetry
• SCHRÖdinger Invariance and Strongly Anisotropic Critical Systems
• Real-time gauge/gravity duality
• Heating up Galilean holography
• Hot Spacetimes for Cold Atoms
• Schr"odinger invariance and space-time symmetries
• Dipoles, Twists and Noncommutative Gauge Theory
• The geometry of Schrödinger symmetry in non-relativistic CFT
• Universal Kaluza-Klein reductions of type IIB to N=4 supergravity in five dimensions
• Type IIB supergravity on squashed Sasaki-Einstein manifolds
• The 192 Solutions of the Heun Equation
• Correlation Functions in Non-Relativistic Holography
• Real-time gauge/gravity duality and ingoing boundary conditions
• Twisted Backgrounds, PP-Waves and Nonlocal Field Theories
• Consistent massive truncations of IIB supergravity on Sasaki-Einstein manifolds
• Short-distance and short-time structure of a unitary Fermi gas
• A consistent truncation of IIB supergravity on manifolds admitting a Sasaki-Einstein structure
• Real-time finite-temperature correlators from AdS/CFT
• Correlation functions in the non-relativistic AdS/CFT correspondence
• Vector Deformations of N=4 Super-Yang-Mills Theory, Pinned Branes, and Arched Strings
• Universal Fermi Gas with Two- and Three-Body Resonances
• Real-Time Correlators and Non-Relativistic Holography
• Geometry of Schroedinger Space-Times II: Particle and Field Probes of the Causal Structure

Cited by in corpus (9)

• On the universal identity in second order hydrodynamics
• On correlation functions in $J\bar{T}$-deformed CFTs
• Schrödinger Holography with and without Hyperscaling Violation
• OPE convergence in non-relativistic conformal field theories
• Lorentzian AdS, Wormholes and Holography
• Asymptotically Schroedinger Space-Times: TsT Transformations and Thermodynamics
• On the 3-point functions of Aging Dynamics and the AdS/CFT Correspondence
• Holographic KMS relations at finite density
• Fermionic Open EFT from Holography