Sum rules and three point functions

Abstract

Sum rules constraining the R-current spectral densities are derived holographically for the case of D3-branes, M2-branes and M5-branes all at finite chemical potentials. In each of the cases the sum rule relates a certain integral of the spectral density over the frequency to terms which depend both on long distance physics, hydrodynamics and short distance physics of the theory. The terms which which depend on the short distance physics result from the presence of certain chiral primaries in the OPE of two R-currents which are turned on at finite chemical potential. Since these sum rules contain information of the OPE they provide an alternate method to obtain the structure constants of the two R-currents and the chiral primary. As a consistency check we show that the 3 point function derived from the sum rule precisely matches with that obtained using Witten diagrams.

41 pages

References in corpus (9)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Bulk viscosity of QCD matter near the critical temperature
• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Spectral sum rules for the quark-gluon plasma
• Sum Rules from an Extra Dimension
• Bulk spectral functions in single and multi-scalar gravity duals
• A shear spectral sum rule in a non-conformal gravity dual
• Shear sum rules at finite chemical potential
• R-charge thermodynamical spectral sum rule in N=4 Yang-Mills theory

Cited by in corpus (5)

• A Practical Mini-Course on Applied Holography
• Thermal one point functions, large $d$ and interior geometry of black holes
• Quantum critical response: from conformal perturbation theory to holography
• A Holographic Model for Quantum Critical Responses
• Spectral sum rules for conformal field theories in arbitrary dimensions