Real-time finite-temperature correlators from AdS/CFT

Abstract

In this paper we use AdS/CFT ideas in conjunction with insights from finite temperature real-time field theory formalism to compute 3-point correlators of N =4super Yang-Mills operators, in real time and at finite temperature. To this end, we propose that the gravity field action is integrated only over the right and left quadrants of the Penrose diagram of the Anti de Sitter-Schwarzschild background, with a relative sign between the two terms. For concreteness we consider the case of a scalar field in the black hole background. Using the scalar field Schwinger-Keldysh bulk-toboundary propagators, we give the general expression of a 3-point real-time Green's correlator. We then note that this particular prescription amounts to adapting the finite-temperature analog of Veltman's circling rules to tree-level Witten diagrams, and comment on the retarded and Feynman scalar bulk-to-boundary propagators.We subject our prescription to several checks: KMS identities, the largest time equation and the zero-temperature limit. When specializing to a particular retarded (causal) 3-point function, we find a very simple answer: the momentum-space correlator is given by three causal (two advanced and one retarded) bulk-to-boundary propagators, meeting at a vertex point which is integrated from spatial infinity to the horizon only. This result is expected based on analyticity, since the retarded n-point functions are obtained by analytic continuation from the imaginary time Green's function, and based on causality considerations.

Second order transport coefficients of nonconformal relativistic fluids in various dimensions from Dp-brane

“…Please note that both of the two scalar fields vanish when p = 3, which is the conformal case that has been solved in [4][5][6][7]. The equations of motion (EOM) which can be derived from (2.10) are the Einstein equation and the EOM of scalar fields φ and A:…”

“…This behavior is mostly studied in twoformalisms that are both developed in 2000s. They are the Minkowskian prescription of AdS/CFT duality [1][2][3][4][5][6] and the fluid/gravity correspondence [7][8][9][10][11][12]. Much progress has been made in calculating transport coefficients in both of these formalisms, for various kinds of relativistic fluids.…”

“…The real-time prescription of AdS/CFT correspondence was proposed in [1], with which Policastro et al were able to get the shear viscosity [2] and the sound wave dispersion relation [3] for the 4d conformal fluid. The second order transport coefficients were derived several years later in [4][5][6][7]14]. Then the 1st and 2nd order transport coefficients of conformal relativistic fluid in other dimensions [10,11,[15][16][17][18], and the coupling constant correction to the transport coefficients caused by higher order terms in bulk action [19][20][21][22][23][24][25][26][27][28][29][30] were also studied.…”

Quantum critical response: from conformal perturbation theory to holography

“…In a conformal field theory, this correlation function is completely fixed up to an overall prefactor A O 0 O 0 O [21,26]:…”

“…., the coefficient C JJ diverges due to a pole in the Γ function. Upon regularization, this implies a logarithm in the momentum space correlator, and so the conductivity: 26) with Λ a UV cutoff scale andC…”