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 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 → ∞ 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. arXiv:1708.00035v2 [hep-th]

Correlations vs connectivity in R-charge

“…Despite the expected lack of classical bridges in the BPS limit, the description of the naked singularity and its phase space interpretation in section 4.2, will allow us to identify the regions in spacetime where such quantum connectivity exists. These are precisely the gray areas in phase space describing the naked singularity in the semiclassical limit 20 .…”

“…In fact, since LLM geometries are determined by the expectation value of the single particle phase space density, typical pure states describing at least N c giant gravitons |Ψ typical can not be distinguished from their ensemble averages when probed by low energy observables in classical gravity [82,[95][96][97]. Hence, the product state |Ψ typical ⊗ |Ψ typical is also effectively captured by figure 15 in 20 When restricting the probe operators O L and O R to be half-BPS SO(4) symmetric, there exist conservation laws that can make correlations (5.3) vanish. From now on, it is assumed that given some density ρ, the choice of probes O L and O R is such that (5.3) does not vanish.…”

“…The effective field theory techniques sharpened in [20] will allow us to circumvent this difficulty. These will be used below to introduce some notion of entanglement between different localised gases of pointlike gravitons and to explore connections to teleportation protocols, connectivity in space and traversability in this single boundary set-up.…”

“…• Consider a single N=4 SYM theory. The effective factorisation of the Hilbert space formulated in [20] describing excitations on top of some reference state, allows to describe an entangled gas of gravitons localised in different regions of the transverse 5sphere. This allows to study quantum mechanical effects in a curved background, the gravity dual to the reference state, such as teleportation between different localised regions in a single boundary theory, with the reference state providing a classical channel between both observers.…”

Emergent classical spacetime from microstates of an incipient black hole

“…This subspace, which behaves like the Fock space for the t k operators, can be regarded as a code subspace for the algebra around the vacuum state. In [29], this code subspace was discussed around special excited states corresponding to rectangular Young tableaus. In matrix model language, this is a closed string representation of the Hilbert space.…”