We will first delve into the massless integrable scattering problem within AdS3/CFT2 set within a 1+1-dimensional short representation. We study Hopf algebraic structures within the context of a modified Poincaré algebra and construct suitable R-matrices both for the undeformed and q-deformed case. We find peculiar connections between the boost operator J and the R-matrices, and study the non-coassociative structure that arises in one particular instance in more detail. We then extend the analysis of the boost operator and its coproduct to the representation-independent case and classify admissible boost (Hopf) algebraic structures. We conclude by analysing in more depth the cases relevant to AdS3 string theory.
Moving on from Hopf algebraic considerations, we consider a particular 3-parameter deformed AdS3 background in the Landau-Lifshitz limit. Constructing an effective field theory from the associated Polyakov action, we obtain an effective Lagrangian up to next-to-leading order in the energy parameter κ. Parametrising the dynamical coordinates by means of a single complex field that we later quantise, we proceed with standard QFT tools, analyse propagator and ground state properties and compute the 2-body S-matrix elements at leading and subleading order in the string tension λ.
In the last part of the talk, we dedicate ourselves to a study in linear algebra and spin chain Hamiltonians. First, we construct an algorithmic framework to find the generalised eigensystem of a defective matrix by perturbing it in such a way that it becomes diagonalisable before analysing its eigensystem, only to then later turn off the perturbation again in a particular way. In doing so, we find that the case of non-singular geometric multiplicity requires particular caution. Having established a rigorous methodology, we apply our machinery to the eclectic spin chain while making use of the Nested Coordinate Bethe Ansatz.
This is a pre-viva talk by Leander Wyss in the Fields, Strings, and Geometry Group at Surrey.