Gauge Theory RG Flows from a Warped Resolved Orbifold

TL;DR

This paper explores the holographic RG flow in gauge-string duality for D3-branes on a resolved orbifold, demonstrating a transition from a warped $AdS_5$ background to the standard $AdS_5\times S^5$, with implications for gauge theory dynamics.

Contribution

It explicitly solves for the warp factor in a warped resolved orbifold, revealing the holographic RG flow between different $AdS_5$ backgrounds and corresponding gauge theories.

Findings

Demonstrates the RG flow from $AdS_5 \times S^5/\IZ_3$ to $AdS_5 \times S^5$

Identifies two scenarios for the RG flow involving Higgsing and confinement

Provides explicit warp factor solutions for the resolved orbifold geometry

Abstract

We study gauge-string duality of D3-branes localized at a point on the resolution of the ALE orbifold $\IC^3/\IZ_3$. By explicitly solving for the warp factor, we demonstrate the holographic RG flow from $AdS_5 \times S^5/\IZ_3$ (far away from the resolution) to the usual $AdS_5\times S^5$ (close to the stack). On the gauge theory side, this maps to the flow between the quiver gauge theory and ${\cal N}=4$ super Yang-Mills. We present two possible scenarios for this RG flow depending on the choice of the VEVs. In particular, one of the scenarios proceeds by two steps involving both Higgsing and confinement.