Semiclassical SL(2) Strings on LLM backgrounds

TL;DR

This paper investigates semiclassical string solutions in LLM geometries, connecting these solutions to non-planar operators in N=4 super-Yang-Mills theory and testing a recent duality proposal involving localized SL(2) excitations.

Contribution

It introduces semiclassical string solutions on LLM backgrounds and relates them to non-planar gauge theory operators, providing a non-trivial check of a recent duality conjecture.

Findings

String solutions are labeled by conserved charges E, J, S.

Solutions correspond to non-planar operators with O(N^2) Z-fields.

In the short string limit, solutions match localized SL(2) excitations in gauge theory.

Abstract

We study semiclassical string solutions that live on white regions of the LLM plane for a generic LLM geometry. These string excitations are labelled by conserved charges E, J and S and are thus holographically dual to operators in the SL(2) sector of N = 4 super-Yang Mills made up of covariant derivatives acting on complex scalar fields Z. On the other hand, the LLM geometry itself is dual to an operator consisting of O(N^2) Z-fields so that the operators dual to our solutions, containing both the stringy excitation and background, are non-planar. In an appropriate short string limit we argue that the string solution we find should be dual to a localised SL(2) excitation in the gauge theory language. This allows us to perform a non-trivial check of the recent proposal that the dynamics of localised excitations should be identical, up to a rescaling of the 't Hooft coupling, to the dynamics of those same excitations in the AdS5xS5 background