Speaker
Description
We study a $q$-deformed ${\rm SU}(N)$ Yang-Mills theory in 2+1 dimensions using the lattice Hamiltonian formalism. The deformation introduces a finite level $k$, which truncates representations and allows the theory to interpolate between a confining regime and a topologically ordered regime. Treating $N$, the Yang-Mills coupling $g$, and $k$ as independent control parameters, we analyze the resulting phase diagram in the large-$N$ limit. In particular, we focus on the scaling behavior governed by the 't Hooft coupling and the ratio $k/N$. A variational mean-field analysis shows that the topologically ordered phase can survive at large $N$ when the cutoff level is scaled appropriately with $N$. This result suggests that quantum-group truncations of non-Abelian gauge theories possess a richer continuum and large-$N$ structure than might be expected from observations at $N = 2$ and $3$. Extending the mean-field perspective beyond the present analysis would further clarify the interplay between confinement and topological order and provide useful benchmarks for future quantum-computational studies of gauge theories.