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

TL;DR

This work extends holographic methods to the non-AdS UV of the Klebanov-Tseytlin background to extract high-energy, non-conformal two-point functions in the dual cascading $N=1$ gauge theory. By analyzing linearized fluctuations around KT, the authors compute the UV behavior of correlators for the R-current and the energy-momentum tensor, revealing a longitudinal component from broken R-symmetry and a trace anomaly from broken conformal symmetry, alongside a massive Goldstone-like vector. The results exhibit characteristic logarithmic enhancements in momentum space, such as $\langle J^R J^R\rangle \sim k^2 \log^3(k/\Lambda)$ and $\langle T T\rangle \sim k^4 \log^3(k/\Lambda)$, and identify a confinement scale $\Lambda$ emerging from the KT geometry. These findings illustrate how holography can probe UV non-conformality, symmetry breaking, and beta-function structure in a realistic, though simplified, gauge theory setting, while highlighting the role of holographic renormalization in fixing finite pieces.

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.