We generalize the color/kinematics duality of flat-space scattering amplitudes to the embedding space formulation of AdS boundary correlators. Kinematic numerators and propagators are replaced with differential operators acting on a scalar contact diagram that is the AdS generalization of the momentum conserving delta function of flat space scattering amplitudes. We show that color/kinematics duality implies differential relations among AdS boundary correlators that naturally generalize the flat space BCJ amplitude relations and verify them for the correlators of Yang-Mills theory and of the Nonlinear Sigma Model through four- and six-points, respectively. For the latter we also find representations of the four- and six-point correlator that manifest the duality. Possible double-copy procedures in AdS space are also discussed.

The objective of this thesis is to study the isotropic XXX-1/2 spin chain model using the Algebraic Bethe Ansatz. To this end, we discuss the concept of integrability as well as the Lax operator and R-matrix, which help generate as many commuting operators in involution as there are degrees of freedom. We establish that the spin chain Hamiltonian belongs to this set and provide a definition of a state vector whose parameters, the Bethe roots, are constrained by a set of equations called the Bethe Ansatz Equations. We show that there is a one-to-one correspondence between the Bethe roots and the eigenfunctions of the system. Next, we proceed to study the nature of the low-lying excitations of both the ferromagnetic and antiferromagnetic model in the thermodynamic limit N → ∞ and show that the Bethe roots can be grouped into complexes or strings, which behave like bound states. We see that integrability is directly related to diffractionless scattering, which is obeyed by systems whose scattering matrices satisfy the Yang-Baxter Equation. In order to provide a more physical interpretation, we calculate the scattering matrix of the two-body problem for a system that satisfies the Yang-Baxter Equation and obtain exchange relations that are identical to those obtained using the Algebraic Bethe Ansatz for the XXX-1/2 spin chain model. Finally, we calculate the scattering matrix for a two-body problem interacting with a delta potential and show that this is the same as what we derived using the Coordinate Bethe Ansatz.