My research project
Integrability, String Theory, Quantum Groups
Research on integrability in the context of AdS/CFT, using ideas from mathematics and physics as well as computational techniques.
In this paper, we studied the boost operator in the setting of su(1|1)2. We find a family of different algebras where such an operator can consistently appear, which we classify according to how the two copies of the su(1|1)2 interact with each other. Finally, we construct coproduct maps for each of these algebras and discuss the algebraic relationships among them.
In this paper we find a host of boost operators for a very general choice of coproducts in AdS3- inspired scattering theories, focusing on the massless sector, with and without an added trigonometric deformation. We find that the boost coproducts are exact symmetries of the R-matrices we construct, besides fulfilling the relations of modified Poincar´e-type superalgebras. In the process, we discover an ambiguity in determining the boost coproduct which allows us to derive differential constraints on our R-matrices. In one particular case of the trigonometric deformation, we find a non-coassociative structure which satisfies the axioms of a quasi-Hopf algebra.