AdS RG-Flow and the Super-Yang-Mills Cascade

TL;DR

This paper explores the holographic duals of various Super-Yang-Mills theories using 5D supergravity, analyzing RG flows and scalar potentials to understand the transition between different supersymmetric phases.

Contribution

It provides a detailed study of scalar potentials and RG flow solutions in 5D supergravity duals of N=4, N=2, and N=1 SYM theories, clarifying the connection to field theory moduli spaces.

Findings

Identification of scalar potentials corresponding to different supersymmetric flows

Analysis of the N=2 moduli space and its deformation to N=1 flows

Distinction of flows based on the end-point potential analysis

Abstract

We study the 5 dimensional SUGRA AdS duals of N=4, N=2 and N=1 Super-Yang-Mills theories. To sequentially break the N=4 theory mass terms are introduced that correspond, via the duality, to scalar VEVs in the SUGRA. We determine the appropriate scalar potential and study solutions of the equations of motion that correspond to RG flows in the field theories. Analysis of the potential at the end of the RG flows distinguishes the flows appropriate to the field theory expectations. As already identified in the literature, the dual to the N=2 theory has flows corresponding to the moduli space of the field theory. When the N=2 theory is broken to N=1 the single flow corresponding to the singular point on the N=2 moduli space is picked out as the vacuum. As the N=2 breaking mass scale is increased the vacuum deforms smoothly to previously analysed N=1 flows.