Geometry of integrable structures and Bethe ansatz

by Andrea Fontanella (University of Padova)

Tuesday 18 Dec 2018, 11:00 → 12:00 Europe/Stockholm

132:028

In this talk, I shall discuss geometric aspects and spectral properties of integrable anti-de Sitter backgrounds. In the first part, I will present a step towards the formulation of a Bethe ansatz in AdS2 x S2 x T6 type IIB superstring. The approach presented will rely on the free-fermion condition and overcome the problem of lack of pseudo-vacuum state, which typically affects N=1 supersymmetric integrable models. In the second part, I will show that the R-matrix in AdS3 x S3 x T6 type IIB superstring must satisfy a first order differential equation, which emerges as a consequence of the pseudo-invariance of the R-matrix under the boost generator of the q-deformed Poincaré superaglebra. This differential equation can be interpreted as a parallel equation for the R-matrix with respect to a particular connection on a fibre bundle. The connection has infinitely many singularities on the base space, and it is flat on the non-singular points. This suggests that the algebraic problem of finding the R-matrix can be rewritten in a geometric language, leading to a potential notion of Universal R-matrix. If time permits, I shall discuss recent progress of an ongoing project in this topic. This talk is based on a work in collaboration with Alessandro Torrielli, arXiv:1706.02634 and arXiv:1608.01631.