On the Canonical c-Function in 4-d Field Theories Possessing Supergravity Duals

TL;DR

This paper investigates the properties of the canonical c-function in 4-dimensional quantum field theories with supergravity duals, focusing on its monotonicity and relation to holographic Green's functions, with findings limited to specific examples.

Contribution

It explores the monotonicity of the canonical c-function in holographic duals, providing insights but lacking a general proof.

Findings

Canonical c-function positivity is clear

Monotonicity is observed in specific examples

No general proof of monotonicity is provided

Abstract

We study monotonicity and other properties of the canonical c-function (defined through the correlator of the energy-momentum tensor) in some holographic duals of 4-d quantum field theories. The canonical c-function and its derivatives are related to the 5-d Green's function of the dual supergravity theory. While positivity of the canonical c-function is obvious, we have not found a general proof of its monotonicity, even though c is monotonic in the few explicit examples we examine in this paper.