LLM Magnons

TL;DR

This paper constructs dual operators for magnon excitations in LLM geometries, reproducing string theory energy predictions through one-loop anomalous dimensions of restricted Schur polynomial combinations.

Contribution

It introduces a method to identify background and excitations in LLM geometries using subgroup and representation choices in operator construction.

Findings

Operators reproduce string magnon energies via anomalous dimensions

Construction uses restricted Schur polynomials with specific subgroup choices

Demonstrates correspondence between geometric excitations and gauge theory operators

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.