Code subspaces for LLM geometries

Abstract

We consider effective field theory around classical background geometries with a gauge theory dual, in the class of LLM geometries. These are dual to half-BPS states of $\mathcal{N}=$ 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite $N$ limit. We further discuss how one can extract the topology of the state beyond $N\to \infty$ and find that uncertainty and entanglement entropy calculations still provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore there is ambiguity in trying to write an operator that describes the metric globally.

35 pages, 3 figures

References in corpus (3)

• From Gravitons to Giants
• On Classification Of The Bubbling Geometries
• Thresholds of Large N Factorization in CFT4 : Exploring bulk spacetime in AdS5

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