Strings and Spins in Deformed AdS/CFT

Abstract

I will present results from three lines of research that I followed during my PhD over the course of 4 publications (2004.02531, 2009.11171, 2102.06419 and 2112.13883).

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.