Gauge/gravity duality

TL;DR

This article surveys how gravity and spacetime can emerge from gauge theories through the AdS/CFT correspondence, illustrating how a 4D ${\cal N}=4$ $SU(N_c)$ gauge theory is dual to IIB string theory on $AdS_5\times S^5$ and how the gauge theory’s RG flow maps to the bulk radial direction. It compiles evidence from operator/state matching, Wilson loops, black hole thermodynamics, and hydrodynamics, and explains the holographic dictionary that relates boundary deformations to bulk fields via $\ell=(4\pi g_s N_c)^{1/4}\ell_s$ and $G\sim \ell^8/N_c^2$. The paper also discusses generalizations to deformed geometries, quiver theories, and other D$p$-brane configurations, showing that emergent gravity and strings persist across a wide class of holographic duals, albeit with boundary-condition–driven variations in the bulk dynamics. Finally, it outlines open questions about the completeness of the dictionary, proof status, and extensions beyond AdS to cosmological spacetimes, framing holography as a powerful but still evolving nonperturbative approach to quantum gravity.

Abstract

We review the emergence of gravity from gauge theory in the context of AdS/CFT duality. We discuss the evidence for the duality, its lessons for gravitational physics, generalizations, and open questions.