A Central Charge for sub-AdS Holography

TL;DR

This paper proposes a way to assign a central charge to sub-AdS regions in holography by relating the AdS length to the long string in D-brane stacks, refining understanding of sub-AdS holography and black hole thermodynamics.

Contribution

It introduces a novel central charge definition for sub-AdS scales using long strings in D-brane stacks, applicable across dimensions and consistent with black hole thermodynamics.

Findings

Central charge associated with sub-AdS scales is derived.

The proposal connects long strings, sub-matrix deconfinement, and compact space effects.

Consistency with black hole thermodynamics and IR/UV duality is demonstrated.

Abstract

We synthesize and sharpen various observations about sub-AdS holography in the literature to associate a central charge to sub-AdS scales of AdS x $X$ geometries. A key ingredient in our proposal is the idea that the AdS length is the length of the long string in a stack of $N$ $backreacted$ D-branes. This allows us to make statements about sub-AdS scales by considering long strings in sub-stacks of $M < N$ branes. Our proposal applies in general dimensions, connects with and refines previous ideas about sub-matrix deconfinement & long strings, makes crucial use of the compact space, and is consistent with the expected thermodynamics of small black holes localized on $X$. Some of our arguments draw intuition from separating branes, and have natural connections to (heating up) the Coulomb branch of the gauge theory. We apply related ideas to non-conformal D-branes at zero and finite temperature, discuss the holographic bound and IR/UV duality in theories with 16 supercharges, and find broad consistency.