LLM magnons

Abstract

We consider excitations of LLM geometries described by coloring the LLM plane with concentric black rings. Certain closed string excitations are localized at the edges of these rings. The string theory predictions for the energies of magnon excitations of these strings depends on the radii of the edges of the rings. In this article we construct the operators dual to these closed string excitations and show how to reproduce the string theory predictions for magnon energies by computing one loop anomalous dimensions. These operators are linear combinations of restricted Schur polynomials. The distinction between what is the background and what is the excitation is accomplished in the choice of the subgroup and the representations used to construct the operator.

Non-perturbative string theory from AdS/CFT

“…The perturbative expansion in this LLM background becomes an expansion in 1 N 2 eff , which suggests that the closed string coupling constant g s has been renormalized. This same effect has also been observed beyond the half-BPS sector [49,50,51,52]. Does this renormalization of N persist when non-perturbative corrections are considered?…”

Exciting LLM geometries

“…We pay careful attention to operator mixing, to give evidence supporting the conclusion that the integrable subsectors are decoupled at large N . This closes an important hole in the analysis of [21]. Finally, we consider how the one loop discussion generalizes when we include higher loops.…”

“…The article [21] argued that matrix elements of the planar dilation operator are identical to matrix elements of the dilatation operator computed using local excitations, localized at corner 8 i of the Young diagram for the LLM geometry, after replacing λ = g 2 Y M N by λ eff = g 2 Y M N eff where N eff is the factor of the first box added to corner i. This again amounts to replacing N → N eff so it is the rule we derived in Section 2.3!…”

“…To excite the geometry in the CFT description, add boxes at a particular corner of the Young diagram describing the LLM geometry [20,21,22]. In string theory we understand this as exciting the giants that condensed to produce the geometry.…”

“…One of the original motivations for this study are the results [21,22,41] which suggest the existence of new integrable subsectors of the CFT. We want to explore (and further establish) the existence of these integrable subsectors.…”