Emergent Sasaki-Einstein geometry and AdS/CFT

TL;DR

This paper explores how Sasaki-Einstein geometries emerge from supergravity in AdS5 and their dual superconformal gauge theories, providing explicit finite N approximations and insights into giant graviton duality.

Contribution

It demonstrates the emergence of Sasaki-Einstein metrics from canonical states in dual CFTs and offers explicit finite N approximations linked to BPS-states.

Findings

Explicit finite N approximations to Sasaki-Einstein metrics.

Connection between BPS-states and geometric emergence.

String theory interpretation of giant graviton duality.

Abstract

We consider supergravity in five-dimensional Anti-De Sitter space $AdS_{5}$ with minimal supersymmetry, encoded by a Sasaki-Einstein metric on a five-dimensional compact manifold $M$. Our main result reveals how the Sasaki-Einstein metric emerges from a canonical state in the dual CFT, defined by a superconformal gauge theory in four dimensional Minkowski space $\mathbb{R}^{3,1}$in the t'Hooft limit where the rank $N$ tends to infinity. We obtain explicit finite $N-$approximations to the Sasaki-Einstein metric, expressed in terms of a canonical (i.e. background free) BPS-state on the gauge theory side. We also provide a string theory interpretation of the BPS-state in question, which sheds new light on the previously noted intriguing duality of giant gravitons.