Spiky Strings and Giant Holes

TL;DR

This paper studies semiclassical string solutions in AdS space with large spin, revealing a duality with spin chain excitations called large and small holes, and derives their dispersion relations.

Contribution

It introduces a new semiclassical string description involving spikes and connects it to spin chain holes, providing a detailed analysis of their dynamics and spectrum.

Findings

Identification of large and small spike excitations in semiclassical strings.

Mapping of large spikes to classical spin chain dynamics.

Derivation of dispersion relations for spike excitations.

Abstract

We analyse semiclassical strings in AdS in the limit of one large spin. In this limit, classical string dynamics is described by a finite number of collective coordinates corresponding to spikes or cusps of the string. The semiclassical spectrum consists of two branches of excitations corresponding to "large" and "small" spikes respectively. We propose that these states are dual to the excitations known as large and small holes in the spin chain description of N=4 SUSY Yang-Mills. The dynamics of large spikes in classical string theory can be mapped to that of a classical spin chain of fixed length. In turn, small spikes correspond to classical solitons propagating on the background formed by the large spikes. We derive the dispersion relation for these excitations directly in the finite gap formalism.