Aspects of emergent geometry in the AdS/CFT context

TL;DR

This paper explores how emergent geometry in AdS/CFT can be understood through a gas of particles on the moduli space of orbifold superconformal field theories, extending techniques from N=4 SYM to orbifolds.

Contribution

It generalizes the emergent geometry analysis from N=4 SYM to orbifold theories using the method of images and measure effects, revealing how particle condensation leads to dual geometries.

Findings

Measure effects induce effective repulsion among particles.

Particles condense into non-trivial vacuum configurations.

These configurations correspond to the emergent geometry of the dual space.

Abstract

We study aspects of emergent geometry for the case of orbifold superconformal field theories in four dimensions, where the orbifolds are abelian within the AdS/CFT proposal. In particular, we show that the realization of emergent geometry starting from the N=4 SYM theory in terms of a gas of particles in the moduli space of vacua of a single D3 brane in flat space gets generalized to a gas of particles on the moduli space of the corresponding orbifold conformal field theory (a gas of D3 branes on the orbifold space). Our main purpose is to show that this can be analyzed using the same techniques as in the N=4 SYM case by using the method of images, including the measure effects associated to the volume of the gauge orbit of the configurations. This measure effect gives an effective repulsion between the particles that makes them condense into a non-trivial vacuum configuration, and it is exactly these configurations that lead to the geometry of X in the AdS x X dual field theory