Exciting LLM Geometries

TL;DR

This paper investigates excitations of LLM geometries from giant graviton condensates, revealing that their emergent low-energy gauge theories exhibit properties identical to planar ${ m extbf{N}=4}$ super Yang-Mills, despite not being identical theories.

Contribution

It provides evidence that the emergent gauge theories from LLM geometries are equivalent to planar ${ m extbf{N}=4}$ super Yang-Mills in key aspects, clarifying their relationship.

Findings

Planar Hilbert spaces are isomorphic.

OPE coefficients vanish in the planar limit.

Spectra of anomalous dimensions match those of planar ${ m extbf{N}=4}$ SYM.

Abstract

We study excitations of LLM geometries. These geometries arise from the backreaction of a condensate of giant gravitons. Excitations of the condensed branes are open strings, which give rise to an emergent Yang-Mills theory at low energy. We study the dynamics of the planar limit of these emergent gauge theories, accumulating evidence that they are planar ${\cal N}=4$ super Yang-Mills. There are three observations supporting this conclusion: (i) we argue for an isomorphism between the planar Hilbert space of the original ${\cal N}=4$ super Yang-Mills and the planar Hilbert space of the emergent gauge theory, (ii) we argue that the OPE coefficients of the planar limit of the emergent gauge theory vanish and (iii) we argue that the planar spectrum of anomalous dimensions of the emergent gauge theory is that of planar ${\cal N}=4$ super Yang-Mills. Despite the fact that the planar limit of the emergent gauge theory is planar ${\cal N}=4$ super Yang-Mills, we explain why the emergent gauge theory is not ${\cal N}=4$ super Yang-Mills theory.