Holographic Correlators in a Flow to a Fixed Point

TL;DR

This paper uses holographic renormalization to analyze correlation functions during a renormalization group flow between two 2D superconformal field theories, revealing insights into the behavior of the C function and resolving existing puzzles.

Contribution

It provides a detailed holographic computation of correlators along the RG flow and compares different proposals for the holographic C function, addressing previous unresolved issues.

Findings

Computed stress-energy tensor correlators along the flow

Constructed and compared Zamolodchikov's C function with holographic proposals

Resolved two puzzles related to five-dimensional supergravity

Abstract

Using holographic renormalization, we study correlation functions throughout a renormalization group flow between two-dimensional superconformal field theories. The ultraviolet theory is an N=(4,4) CFT which can be thought of as a symmetric product of U(2) super WZW models. It is perturbed by a relevant operator which preserves one-quarter supersymmetry and drives the theory to an infrared fixed point. We compute correlators of the stress-energy tensor and of the relevant operators dual to supergravity scalars. Using the former, we put together Zamolodchikov's C function, and contrast it with proposals for a holographic C function. In passing, we address and resolve two puzzles also found in the case of five-dimensional bulk supergravity.