Giant Magnons and Giant Gravitons

Abstract

In this thesis we shall present work concerning the description of the emergence of solitonic fundamental strings from stable, finite energy, compact D3-branes in a subspace of and their subsequent interaction. We work in the planar limit and focus on states of large angular momentum corresponding to large R-charge in the dual gauge theory.

We begin by constructing the full set of boundary giant magnons on attached to the maximal giant graviton by mapping from the general solution to static sine-Gordon theory on the interval. We then compute the values of the anomalous dimension, , of the dual gauge theory operators at finite , examining the behaviour of the leading order corrections when is large.

We then consider the Born-Infeld theory of the giant graviton itself coupled to the background 5-form flux. Constructing BIon spike solutions that correspond to the world volume description of the boundary giant magnons we find a limit amenable to analysis which returns the full range of behaviour exhibited at finite .

Finally we produce the open strings on that correspond to the solutions of integrable boundary sine-Gordon theory. Relating the boundary parameters in a way that ensures a given set of string boundary conditions we describe the scattering of giant magnons with non-maximal giant gravitons and calculate the leading contribution to the associated magnon scattering phase. Our method necessarily describes all integrable scatterings of giant magnons with giant gravitons.