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arXiv:2601.03843

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

Tomoya Hayata, Yoshimasa Hidaka, Hiromasa Watanabe

hep-latcond-mat.str-elhep-thquant-phSubmitted Jan 7, 2026• Announced Jan 8, 2026
arXivHTMLPDF

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.

Comments
7+4 pages, 5+2 figures, 2+1 tables; analysis code will be made publicly available on GitHub after publication

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