AdS$_3\times$S$^3$ magnons in the symmetric orbifold

TL;DR

This paper identifies specific collective modes in the symmetric orbifold that correspond to AdS$_3\times$S$^3$ magnons, enhancing understanding of the duality between string theory excitations and orbifold conformal states.

Contribution

It introduces a detailed correspondence between AdS$_3\times$S$^3$ excitations and collective eigenmodes in the symmetric orbifold, including new long modes involving superpositions of fractional torus modes.

Findings

Identification of collective modes matching AdS$_3\times$S$^3$ excitations

Discovery of long collective eigenmodes involving superpositions

Reduction of modes to fractional $\mathcal{N}=4$ modes at integer momentum

Abstract

The AdS$_3\times$S$^3$ excitations of string theory on AdS$_3\times$S$^3\times \mathbb{T}^4$ are identified with certain collective modes in the dual symmetric orbifold. Our identification follows from a careful study of the conformal eigenstates in the perturbed orbifold theory. We find that, in addition to the fractional torus modes (that correspond to the torus excitations in the dual AdS spacetime), there are `long' collective eigenmodes that involve a superposition of products of fractional torus modes, and that are in natural one-to-one correspondence with the expected AdS$_3\times$S$^3$ excitations. These collective modes are deformations of (fractional) $\mathcal{N}=4$ modes, to which they reduce for integer momentum.