Holographic thermal correlators from supersymmetric instantons

Abstract

We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory with four fundamental hypermultiplets. The result is amenable to numerical evaluation upon truncating the number of instantons in the convergent expansion of the partition function. We also examine it analytically in various limits. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we compute the OPE data of heavy-light double-twist operators. We compare our prediction to the perturbative results available in the literature and find perfect agreement.

arXiv comment9 pages + appendices, 2 figures. v2: typos corrected, references added

References in corpus (90)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Quasinormal modes of black holes and black branes
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Lectures on holographic methods for condensed matter physics
• Eternal Black Holes in AdS
• Black holes and the butterfly effect
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Nonlinear Fluid Dynamics from Gravity
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• From AdS/CFT correspondence to hydrodynamics
• Holography from Conformal Field Theory
• Conformal Partial Waves and the Operator Product Expansion
• The approach to thermal equilibrium in quantized chaotic systems
• The Analytic Bootstrap and AdS Superhorizon Locality
• Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm
• Analyticity in Spin in Conformal Theories
• Two and three-point functions in Liouville theory
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Convexity and Liberation at Large Spin
• Universality of Long-Distance AdS Physics from the CFT Bootstrap
• Instantons and recursion relations in N=2 Susy gauge theory
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
• The Black Hole Singularity in AdS/CFT
• Virasoro Conformal Blocks and Thermality from Classical Background Fields
• Quantization of Integrable Systems and Four Dimensional Gauge Theories
• Holographic quantum matter
• Light-ray operators in conformal field theory
• Small Kerr-anti-de Sitter black holes are unstable
• AdS/CFT correspondence, quasinormal modes, and thermal correlators in N=4 SYM
• Gauge symmetry breaking on orbifolds
• On quasinormal modes of small Schwarzschild-Anti-de-Sitter black hole
• A spacetime derivation of the Lorentzian OPE inversion formula
• Conformal Partial Waves: Further Mathematical Results
• Gauge Theory Loop Operators and Liouville Theory
• Black hole scrambling from hydrodynamics
• Many-body chaos and energy dynamics in holography
• The complex life of hydrodynamic modes
• Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers
• Excursions beyond the horizon: Black hole singularities in Yang-Mills theories (I)
• Recursion relations in CFT and N=2 SYM theory
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• A Bohr-Sommerfeld quantization formula for quasinormal frequencies of AdS black holes
• The Conformal Bootstrap at Finite Temperature
• Asymptotics of thermal spectral functions
• Matone's Relation in the Presence of Gravitational Couplings
• Irregular Liouville correlators and connection formulae for Heun functions
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Conformal Bootstrap At Large Charge
• Diving into a holographic superconductor
• The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
• QNMs of branes, BHs and fuzzballs from Quantum SW geometries
• Proper time to the black hole singularity from thermal one-point functions
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses
• Hydrodynamic Long-Time tails From Anti de Sitter Space
• Heavy Operators and Hydrodynamic Tails
• Universal Lowest-Twist in CFTs from Holography
• Opers, surface defects, and Yang-Yang functional
• Black Holes, Heavy States, Phase Shift and Anomalous Dimensions
• Gravitational orbits, double-twist mirage, and many-body scars
• Integrability and cycles of deformed $\mathcal{N}=2$ gauge theory
• Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
• Subleading Eikonal, AdS/CFT and Double Stress Tensors
• Probing Universalities in d>2 CFTs: from Black Holes to Shockwaves
• A slow review of the AGT correspondence
• Black Holes and Conformal Regge Bootstrap
• Pole skipping away from maximal chaos
• Leading Multi-Stress Tensors and Conformal Bootstrap
• Exact WKB methods in $SU(2)$ $N_f=1$
• Holographic Correlators at Finite Temperature
• Thermalization in Large-N CFTs
• Heavy-light Bootstrap from Lorentzian Inversion Formula
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Thermal Stress Tensor Correlators, OPE and Holography
• Model-Dependence of Minimal-Twist OPEs in $d>2$ Holographic CFTs
• ISCOs in AdS/CFT
• Near Lightcone Thermal Conformal Correlators and Holography
• Bands and gaps in Nekrasov partition function
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• CFT correlators, $\mathcal{W}$-algebras and Generalized Catalan Numbers
• More Analytic Bootstrap: Nonperturbative Effects and Fermions
• Toward the Pole
• A new method for exact results on Quasinormal Modes of Black Holes
• The Heun functions as a modern powerful tool for research in different scientific domains
• More on Heavy-Light Bootstrap up to Double-Stress-Tensor

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• Thermal Product Formula for Shear Modes
• Resummation of Multi-Stress Tensors in Higher Dimensions
• Finite Temperature at Finite Places
• Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry
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