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)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.

Relativistic Hydrodynamics: A Singulant Perspective

“…Thus, finding a way to incorporate properties of the 'global' analytic structure of ω(k) -rather than just analyticity at k = 0 -may result in a more constrained region of transport coefficient space. For instance, a recent conjecture for the analytic structure of chaotic large N thermal two-point functions [23] may have bearing on the analytic structure of ω(k). Analogously, it is a conjecture in the S-matrix bootstrap programme that the amplitudes are 'maximally analytic', and given this additional information allows for stronger constraints; see for example [14,24,25].…”

Boundary signature of singularity in the presence of a shock wave

“…where there is a branch point associated with every C a i in the u a plane at u i and the branch cut is chosen to extend to infinity from u i . 24 The branch cut associated with u L − u R is chosen to be at Im(u L − u R ) < 0, Re(u L ) = Re(u R ) = 0. The analytic structure is therefore in agreement with what was discussed in Section 4.3.1.…”

Holographic torus correlators in AdS3 gravity coupled to scalar field

“…The investigation of scalar field solutions within a fixed gravitational background has been extensively explored in numerous works [22,[44][45][46][47][48][49][50][51][52][53]. The majority of these studies utilize the…”