Correlation functions in a cascading N=1 gauge theory from supergravity

TL;DR

This paper analyzes correlation functions in a non-conformal N=1 gauge theory using supergravity fluctuations around the warped conifold, revealing insights into R-symmetry breaking and conformal symmetry violation at high energies.

Contribution

It applies AdS/CFT techniques to a non-AdS supergravity background to compute high energy correlators, including R-current and energy-momentum tensor functions.

Findings

R-current 2-point function has a longitudinal component due to R-symmetry breaking.

Computed the mass of the Goldstone vector matching theoretical predictions.

High energy energy-momentum tensor correlator shows trace part from broken conformal symmetry.

Abstract

We study fluctuations around the warped conifold supergravity solution of Klebanov and Tseytlin [hep-th/0002159], known to be dual to a cascading N=1 gauge theory. Although this supergravity background is not asymptotically AdS, corresponding to a non-conformal field theory, it is possible to apply the usual methods of AdS/CFT duality to extract the high energy behavior of field theory correlators by solving linearized equations of motion for fluctuations around the background. We consider the Goldstone vector dual to the anomalous R-symmetry current and compute its mass, which exactly matches the general prediction of [hep-th/0009156]. We find the high energy 2-point functions for the R-current and two other vectors. As expected, the R-current 2-point function has a longitudinal part because R-symmetry is broken. We also calculate the high energy 2-point function of the energy-momentum tensor from fluctuations of modes in the graviton sector. This 2-point function has a trace part corresponding to broken conformal symmetry.