There is a class of representations of quantum groups, referred to as prefundamental representations, that plays an important role in the solution of integrable models. The first example of such representations was given by V. Bazhanov, S. Lukyanov and A. Zamolodchikov in the context of two dimensional conformal field theory in order to construct Baxter Q-operators as transfer matrices. At the same time, there is a rather exceptional quantum group that governs the integrable structure of the one dimensional Hubbard model and plays a fundamental role in the AdS/CFT correspondence. In this talk I will introduce prefundamental representations for this quantum group, explain their basic properties and discuss some of their applications. ------------- Part of London Integrability Journal Club. New participants please register at integrability-london.weebly.com to receive the link. (Registration is needed only once).

I will present some results on the 1d Super-Conformal Field Theory (SCFT) living on a 1/2-BPS line defect in a 4d N=4 SCFT. The main realization of this setup being Wilson lines in N=4 Super-Yang-Mills (SYM). After reviewing what the modern numerical bootstrap have to say about this problem I will describe how analytic bootstrap methods can efficiently produce the perturbative expansion at strong coupling in the planar theory. NOTE: This will be an online seminar using Zoom. Please register at integrability-london.weebly.com to receive the link

To any four-dimensional N=2 super-conformal field theory (SCFT) one can canonically associate a two-dimensional vertex operator algebra (VOA). This provides a powerful framework for the analysis of SCFTs and leads to surprising predictions for a large new class of VOAs. In this talk I will present remarkable free field realizations of the relevant VOAs which mirror the effective field theory description of the corresponding four dimensional theory on the Higgs branch of its moduli space of vacua.

Any four dimensional N=2 superconformal field theory (SCFT) contains a subsector of local operator which is isomorphic to a two dimensional chiral algebra. If the 4d theory possesses N=3 or N= 4 superconformal symmetry, the corresponding chiral algebra is an extension the N=2 or (small) N=4 super-Virasoro algebra respectively. In this talk I will present some results on the classification of N=4 chiral algebras and discuss if they can correspond to a 4d theory.