The AdS/CFT correspondence offers a unique possibility for the nonperturbative investigation of gauge theories, through their conjectured equivalence to string theories. In the past years, there has been tremendous progress in the computation of the anomalous dimensions of gauge theory operators, or equivalently energies of string states, thanks to the integrable structures that emerge in the 't Hooft limit.In this thesis, we study the two main manifestations of integrability in gauge/string dualities, namely solitons in string theory and spin chains in gauge theory. We first review the emergence of an integrable spin chain in maximally supersymmetric Yang-Mills theory, and the identification of the string dual to a single excitation in a certain limit, the `giant magnon' solution. We then semiclassicaly quantize the solution and obtain the first quantum correction to its energy, in agreement with expectations based on symmetry. The fact that the string configuration in question amounts to a single solitary wave of the string sigma model, subsequently allows us to use a nonlinear superposition method known as dressing, in order to construct a general formula describing the scattering of an arbitrary number of solitons. We further generalize our solutions for the most recent instance of a gauge/string duality, involving the 3-dimensional super Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM).We also study the symmetry of the integrable spin chain arising in the latter duality. In particular we compute how the Hilbert space of spin chain states of length up to 4, decomposes into irreducible representations of the superconformal group, for which we also obtain the characters. This structural information enables us to calculate the leading correction to the Hagedorn temperature of weakly coupled planar ABJM theory, and more importantly serves as a tool for the detailed spectroscopic analysis of anomalous dimensions, which we turn to next. Employing a combination of Bethe Ansatz and Hamiltonian diagonalization techniques, we find the spectrum of low-lying states of length 4 at 2 loops, and identify three new sequences of rational eigenvalues.
Papathanasiou, Georgios,
"Solitons and Spin Chains in Gauge/String Dualities"
(2011).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0TD9VMG
