Cascading RG Flows from New Sasaki-Einstein Manifolds

TL;DR

This work extends gauge/gravity duality to the new Sasaki-Einstein manifolds $Y^{p,q}$ by constructing warped IIB backgrounds with fluxes corresponding to $N$ D3-branes and $M$ wrapped D5-branes at the cone apex. The authors derive an explicit warp factor $h(r,y)$ and show that the dual quiver gauge theories exhibit cascading RG flows with $N$ decreasing in steps controlled by Seiberg duality, matching the supergravity beta-functions. They develop and utilize a harmonic $(2,1)$ form to support $(2,1)$ flux, perform a detailed beta-function matching between gravity and field theory, and analyze cascades for $Y^{p,p-1}$ and $Y^{p,1}$, including a baryonic branch in the IR. The results provide concrete checks of the AdS/CFT correspondence in a broad family of geometries and reveal rich IR dynamics, including confinement-like behavior and baryonic moduli spaces, tied to the geometric data of $Y^{p,q}$.

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.

Figures (4)

• Figure 1: Shown are a) the unit cell $\sigma$; b) the unit cell $\tau$; and c) the quiver for $Y^{4,3}$, $\sigma \tilde{\tau} \sigma \tilde{\sigma}$.
• Figure 2: The quiver for $Y^{4,3}$ reproduced from Figure 4 of Benvenuti. This quiver is identical to Figure 1c.
• Figure 3: The quiver theory for $Y^{4,1}$, involving three $\tau$ unit cells and one $\sigma$ unit cell.
• Figure 4: Seiberg duality for the $Y^{p,1}$ quiver: $(\cdots \tau \tilde{\tau} \sigma \tilde{\tau} \cdots )\to (\cdots \tau \tilde{\sigma} \tau \tilde{\tau} \cdots )$.