Quantum Group Symmetry in Multiple Chern-Simons Theory on a Torus

TL;DR

This paper explores the emergence of $w_ abla$ and $sl_q(2)$ symmetries in multiple Chern-Simons theory on a torus, linking algebraic structures to the dynamics of non-integrable phases and Wilson line operators.

Contribution

It demonstrates how these algebraic symmetries originate from the dynamics of phases in Chern-Simons theory and constructs their generators from Wilson lines.

Findings

Algebraic structures arise from non-integrable phase dynamics

Generators constructed from Wilson line operators

Vacuum states form cyclic representations of $sl_q(2)$

Abstract

We discuss $w_\infty$ and $sl_q(2)$ symmetries in multiple Chern-Simons theory on a torus. It is shown that these algebraic structures arise from the dynamics of the non-integrable phases of the Chern-Simons fields. The generators of these algebras are constructed from the Wilson line operators corresponding to these phases. The vacuum states form the basis of cyclic representation of $sl_q (2)$.