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

Abstract

We discuss $w_{\infty }$ and $s{l}_q(2)$ 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 $s{l}_q(2)$.

12 pages. Plain Tex.

References in corpus (2)

• Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field
• $W_{\infty }$ algebra in the integer quantum Hall effects

Cited by in corpus (2)

• Finite-dimensional Schwinger basis, deformed symmetries, Wigner function, and an algebraic approach to quantum phase
• Recurrent dynamical symmetry breaking and restoration by Wilson lines at finite densities on a torus