Higher spins in 2d conformal field theory

The underlying symmetry of two-dimensional conformal field theory is the Virasoro algebra. In certain situations this infinite dimensional symmetry is further extended by higher spin currents resulting in so-called W-algebras. Such algebras are closely related to quantum integrability and recently have been found to describe subsectors of four-dimensional supersymmetric gauge theories. The aim of this project is in particular to focus on the integrable aspects of these higher spin symmetries and to apply methods of algebraic Bethe ansatz to these 2d quantum field theory models.

The candidate should have good knowledge of quantum mechanics and basics of quantum field theory as well as basic representation theory. He should also be willing to learn the necessary 2d conformal theory that is needed for this project.

References: [1] D. Sénéchal, P. Di Francesco, P. Mathieu – Conformal Field Theory (Springer, 1996)
[2] P. Bouwknegt, K. Schoutens – W symmetry in conformal field theory (Phys.Rept. 223 (1993) 183–276, arXiv: hep-th/9210010)
[3] T. Procházka – W-symmetry, topological vertex and affine Yangian (JHEP 10 (2016) 077, arXiv: 1512.07178)
[4] B. Feigin, M. Jimbo, E. Mukhin – Integrals of motion from quantum toroidal algebras (J.Phys.A 50 (2017) 46, 464001, arXiv: 1705.07984)
[5] K. Costello, D. Gaiotto – Twisted Holography (arXiv: 1812.09257)