Holographic correlation functions at finite density and/or finite temperature

Abstract

We calculate holographically one and two-point functions of scalar operators at finite density and/or finite temperature. In the case of finite density and zero temperature we argue that only scalar operators can have non-zero VEVs. In the case in which both the chemical potential and the temperature are finite, we present a systematic expansion of the two-point correlators in powers of the temperature T and the chemical potential $\Omega$. The holographic result is in agreement with the general form of the OPE which dictates that the two-point function may be written as a linear combination of the Gegenbauer polynomials $C_J^{(1)}(\xi )$ but with the coefficients depending now on both the temperature and the chemical potential, as well as on the CFT data. The leading terms in this expansion originate from the expectation values of the scalar operator ${\varphi }^2$, the R-current ${\mathcal{J}}_{{\varphi }_3}^{\mu }$ and the energy-momentum tensor $T^{\mu \nu }$. By employing the Ward identity for the R-current and by comparing the appropriate term of the holographic result for the two-point correlator to the corresponding term in the OPE, we derive the value of the R-charge density of the background. Compelling agreement with the analysis of the thermodynamics of the black hole is found. Finally, we determine the behaviour of the two-point correlators, in the case of finite temperature, and in the limit of large temporal or spatial distance of the operators.

arXiv comment1+31 pages

References in corpus (27)

• Implications of Conformal Invariance in Field Theories for General Dimensions
• The Black Hole Singularity in AdS/CFT
• The Coulomb Branch of Gauge Theory from Rotating Branes
• Holographic Particle Detection
• On geodesic propagators and black hole holography
• Extremal surfaces as bulk probes in AdS/CFT
• Thermodynamics of spinning D3-branes
• Excursions beyond the horizon: Black hole singularities in Yang-Mills theories (I)
• The Conformal Bootstrap at Finite Temperature
• On correlation functions of operators dual to classical spinning string states
• Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography
• Bulk-cone singularities & signatures of horizon formation in AdS/CFT
• Near-BPS-Saturated Rotating Electrically Charged Black Holes as String States
• Thermodynamics of Spinning Branes and their Dual Field Theories
• Proper time to the black hole singularity from thermal one-point functions
• Two and three-point correlators of operators dual to folded string solutions at strong coupling
• Supergravity and the jet quenching parameter in the presence of R-charge densities
• Correlation functions in the non-relativistic AdS/CFT correspondence
• New Compactifications of Supergravities and Large N QCD
• SL(2) sector: weak/strong coupling agreement of three-point correlators
• Correlation functions in finite temperature CFT and black hole singularities
• Holography of Two-point Functions in the Spinning String/Spin Chain Correspondence
• Constraining quantum critical dynamics: 2+1D Ising model and beyond
• Thermal one-point functions and single-valued polylogarithms
• Holographic three-point correlators in the Schrodinger/dipole CFT correspondence
• A Holographic Model for Quantum Critical Responses
• Correlators of massive string states with conserved currents

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