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 mathcal{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 mathcal{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 mathcal{N}=4 super Yang-Mills. Despite the fact that the planar limit of the emergent gauge theory is planar mathcal{N}=4 super Yang-Mills, we explain why the emergent gauge theory is not mathcal{N}=4 super Yang-Mills theory.
Highlights
Background dependenceIrreducible representations of the symmetric group Sn are labeled by Young diagrams with n boxes
There are three observations supporting this conclusion: (i) we argue for an isomorphism between the planar Hilbert space of the original N = 4 super Yang-Mills and the planar Hilbert space of the emergent gauge theory, (ii) we argue that the operator product expansion (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 N = 4 super Yang-Mills
Since OPE coefficients are read from three point functions, the OPE coefficients vanish in the planar limit of both N = 4 super Yang-Mills and the emergent gauge theory
Summary
The LLM geometry is described by a CFT operator with a bare dimension of order N 2 It is a Schur polynomial [13] labeled by a Young diagram with O(N 2) boxes and O(1) corners. The excitations are obtained by adding boxes to the Young diagram describing the background, at a specific location They are localized in the dual gravitational description, at a specific radius on the bubbling plane [21, 22]. The excitations belonging to the localized Hilbert spaces play a central role in our study These are the Hilbert spaces of the emergent gauge theories. We give a bijection between the states belonging to the planar Hilbert space of an emergent gauge theory, and the states of the planar limit of the original CFT without background. Thanks to the map between correlation functions, any statement about the planar limit that can be phrased in terms of correlators, immediately becomes a statement about the planar emergent gauge theories that arise in the large N but non-planar limits we consider
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