Sketches of emergent geometry in the gauge/gravity duality

TL;DR

This paper explores three different notions of emergent geometry in gauge/gravity duality, showing how properties of gauge theory configurations can be matched to geometric features in the gravity dual.

Contribution

It introduces and compares three approaches to emergent geometry in gauge/gravity duality, connecting gauge theory effective actions to gravity space-time features.

Findings

Properties of probe actions can be localized in the gravity dual.

Emergent geometries can be derived from gauge theory configurations.

Different examples demonstrate the correspondence between gauge and gravity descriptions.

Abstract

In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe or excitation around some configuration in gauge theory which can be argued to be localized at a particular position in the gravity dual, and match this description to various degrees of accuracy in the gravity dual. The three examples discussed are giant gravitons in $AdS_5\times S^5$, open strings stretching between these giants and the probe dynamics of a D0 brane in the presence of a thermal matrix configuration of the BFSS matrix model.