Giant magnons and giant gravitons

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 $AdS_{5}\times S^{5}$ and their subsequent interaction. We work in the planar limit and focus on states of large angular momentum $J$ corresponding to large R-charge in the dual gauge theory. We begin by constructing the full set of boundary giant magnons on $\mathbb{R}\times S^{2}$ attached to the maximal $Z=0$ 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, $\Delta-J$, of the dual gauge theory operators at finite $J$, examining the behaviour of the leading order corrections when $J$ 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 $J$. Finally we produce the open strings on $\mathbb{R}\times S^{2}$ 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 $Y=0$ 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.EThOS - Electronic Theses Online ServiceGBUnited Kingdo