Gauge/gravity duality and RG flows in 5d gauge theories

TL;DR

The paper develops a holographic framework for RG flows in 4d $\mathcal{N}=2$ and 5d theories with eight supercharges, triggered by mesonic or baryonic VEVs. By solving a PDE for the warp factor on singular and resolved cones under AdS/CFT, it extracts the operator spectra and matches gravity modes to gauge-theory operators, including the appearance of Goldstone bosons in baryonic phases. In 4d, mesonic flows on the singular cone and baryonic flows on the resolved cone yield operator dimensions $\Delta=2l+n$ and $\Delta=2l+2q$, respectively; in 5d, mesonic flows give $\Delta=3l$ while baryonic flows (available only in the NVS case) yield $\Delta=3l$ for mesonic-type modes and $\Delta=\frac{3}{2}N$ for baryons, with the Goldstone mode realized by brane configurations. The analysis reveals a consistent picture: boundary conditions on the PDE crucially fix the spectrum, the singularity controls operator dimensions in 5d, and the resolved geometry encodes spontaneous baryonic symmetry breaking with explicit brane realizations of the condensates and their Goldstone bosons.

Abstract

We discuss RG flows in 5d gauge theories triggered either by VEV's of mesonic or baryonic operators. As a warm-up, we explicitly discuss the counterpart of these flows in 4d gauge theories with $\mathcal{N}=2$ supersymmetry by focusing on the $A_1$ theory. As opposed to the $\mathcal{N}=1$ case, in cases with 8 supercharges we need to solve a more involved PDE. In the 5d case the boundary conditions for such equation play a crucial role in order to reproduce the expected spectrum.