A Primer to Categorical Symmetries and Their Application to QCD in Two Dimensions

• Main Author: Olofsson, Rikard
• Format: Others
• Language: English
• Published: Uppsala universitet, Teoretisk fysik 2021
• Subjects: category theory; fusion category; topological defect lines; rational conformal field theory; Wess Zumino Witten-model; QCD; Other Physics Topics; Annan fysik
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-458657

We introduce the formalism of categorical symmetries, and examine how these appear in quantum field theories. We discuss rational conformal field theories and their Verlinde lines, with the critical Ising model as an example. We introduce Wess Zumino Witten models and affine Lie algebras. An algorithm for the fusion rules is presented. We use bosonization to realise two dimensional adjoint SU(N) QCD as a WZW coset model plus a kinetic term for the gauge field. We argue that the infrared theory has degenerate vacua acted upon by a non-negative integer valued matrix representation of a categorical symmetry. We compute generators for these matrices for gauge groups SU(3) and SU(4).