Holographic R-symmetric flows and the \tau_U conjecture

TL;DR

This paper explores the holographic dual of a conjecture about R-symmetric RG flows in 4D supersymmetric theories, analyzing a bulk quantity's monotonicity to support the  conjecture and its behavior in gapped theories.

Contribution

It introduces a holographic approach to study the  conjecture for R-symmetric RG flows, defining a bulk quantity that interpolates between UV and IR fixed points and analyzing its monotonicity.

Findings

The bulk quantity is monotonic for flows to an interacting IR fixed point.

In gapped theories, monotonicity holds up to a finite scale reflecting the gap.

The analysis supports the  conjecture in a holographic context.

Abstract

We discuss the holographic counterpart of a recent conjecture regarding R-symmetric RG-flows in four-dimensional supersymmetric field theories. In such theories, a quantity \tau_U can be defined at the fixed points which was conjectured in arXiv:1109.3279 to be larger in the UV than in the IR, \tau_U^{UV} > \tau_U^{IR}. We analyze this conjecture from a dual supergravity perspective: using some general properties of domain wall solutions dual to R-symmetric RG flows, we define a bulk quantity which interpolates between the correct \tau_U at the UV and IR fixed points, and study its monotonicity properties in a class of examples. We find a monotonic behavior for theories flowing to an interacting IR fixed point. For gapped theories, the monotonicity is still valid up to a finite value of the radial coordinate where the function vanishes, reflecting the gap scale of the field theory.