Phases of the $q$-deformed $\mathrm{SU}(N)$ Yang-Mills theory at large $N$

• URL: http://arxiv.org/abs/2601.03843v1
• Date: Wed, 07 Jan 2026 12:06:40 GMT
• Title: Phases of the $q$-deformed $\mathrm{SU}(N)$ Yang-Mills theory at large $N$
• Authors: Tomoya Hayata, Yoshimasa Hidaka, Hiromasa Watanabe,
• Abstract summary: Yang-Mills theory is characterized by three parameters: the number of colors $N$, the coupling constant $g$, and the level $k$.<n>By treating these as tunable parameters, we explore how key properties of the theory, such as confinement and topological order, emerge in different regimes.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the $(2+1)$-dimensional $q$-deformed $\mathrm{SU}(N)_k$ Yang-Mills theory in the lattice Hamiltonian formalism, which is characterized by three parameters: the number of colors $N$, the coupling constant $g$, and the level $k$. By treating these as tunable parameters, we explore how key properties of the theory, such as confinement and topological order, emerge in different regimes. Employing a variational mean-field analysis that interpolates between the strong- and weak-coupling regimes, we determine the large-$N$ phase structure in terms of the 't Hooft coupling $λ_\mathrm{tH}=g^2N$ and the ratio $k/N$. We find that the topologically ordered phase remains robust at large $N$ under appropriate scalings of these parameters. This result indicates that the continuum limit of large-$N$ gauge theory may be more intricate than naively expected, and motivates studies beyond the mean-field theory, both to achieve a further understanding of confinement in gauge theories and to guide quantum simulations of large-$N$ gauge theories.

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