Cascading RG Flows from New Sasaki-Einstein Manifolds

TL;DR

This paper constructs explicit supergravity solutions describing cascading RG flows for D3-branes on cones over Sasaki-Einstein manifolds $Y^{p,q}$, matching dual gauge theory beta functions and exploring dibaryon operators.

Contribution

It provides the first explicit supergravity solutions for cascading RG flows on $Y^{p,q}$ spaces, confirming dual gauge theory predictions and analyzing dibaryon operators.

Findings

Supergravity solutions for all p, q describing RG cascades.

Exact match between supergravity and gauge theory beta functions.

Analysis of dibaryon operators and their duals.

Abstract

In important recent developments, new Sasaki-Einstein spaces $Y^{p,q}$ and conformal gauge theories dual to $AdS_5\times Y^{p,q}$ have been constructed. We consider a stack of N D3-branes and M wrapped D5-branes at the apex of a cone over $Y^{p,q}$. Replacing the D-branes by their fluxes, we construct asymptotic solutions for all p and q in the form of warped products of the cone and $R^{3,1}$. We show that they describe cascading RG flows where N decreases logarithmically with the scale. The warp factor, which we determine explicitly, is a function of the radius of the cone and one of the coordinates on $Y^{p,q}$. We describe the RG cascades in the dual quiver gauge theories, and find an exact agreement between the supergravity and the field theory beta functions. We also discuss certain dibaryon operators and their dual wrapped D3-branes in the conformal case M=0.