Dyon Condensation at $θ=2π$ from Wilson-'t Hooft Loops in Yang-Mills Theory

Hiromasa Watanabe; Issaku Kanamori; Okuto Morikawa; Yuki Nagai; Yuya Tanizaki; Akio Tomiya

Home/Archive/arXiv

arXiv · 2610.31281

Dyon Condensation at $θ=2π$ from Wilson-'t Hooft Loops in Yang-Mills Theory

Hiromasa Watanabe·Issaku Kanamori·Okuto Morikawa·Yuki Nagai·Yuya Tanizaki·Akio Tomiya

View original source ↗Read source document ↗Export metadata ↓

Abstract

Although Yang--Mills theories at $θ$ and $θ+2π$ are physically equivalent, their periodicity is realized nontrivially in the presence of a background field for the $1$-form center symmetry. The confining vacua at $θ=0$ and $2π$ are therefore expected to have distinct symmetry-protected topological labels. We test this expectation in $SU(2)$ lattice Yang--Mills theory by measuring 't~Hooft and dyonic Wilson--'t~Hooft loops at $θ=2π$. A $1$-form-covariant DBW2 flow makes the global reweighting factor numerically benign while retaining the physical non-integer topological charge in a defect ensemble. The dyonic loop exhibits a clear perimeter-law plateau on two lattice volumes. The direct 't~Hooft-loop signal is noise-limited but has the magnitude and distance dependence expected for an area law. Taken together with the Wilson--'t~Hooft classification, these results provide numerical evidence for the dyonic oblique-confinement pattern at $θ=2π$. This talk is based on our recent paper (arXiv:2606.13428).

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Hiromasa Watanabe, Issaku Kanamori, Okuto Morikawa, Yuki Nagai, Yuya Tanizaki, Akio Tomiya. 2026-10-22. Dyon Condensation at $θ=2π$ from Wilson-'t Hooft Loops in Yang-Mills Theory. https://arxiv.org/abs/2610.31281

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Spontaneous chiral-symmetry breaking in four-dimensional QCD with $A_x=A_y=0$ projection in dimensional reduction gauge

We investigate spontaneous chiral-symmetry breaking in four-dimensional (4D) QCD in the dimensional reduction (DR) gauge, defined so as to minimize $R_{\mathrm{DR}}\equiv~\int d^{4}s ~ \mathrm{Tr} \left[ A_{x}^{2}(s) + A_{y}^{2}(s) \right]$. We consider ``$tz$-projection" of $A_{x,y}(s) \to 0$ and ``$xy$-projection" of $A_{t,z}(s) \to 0$, respectively, for the gauge configuration generated in the DR gauge, in a similar sense to Abelian, monopole and photon projections in the maximally Abelian gauge. The chiral condensate is estimated from the low-lying Dirac-eigenvalue density $ρ(λ)$ using the Banks-Casher relation. By the $tz$-projection in the DR gauge, the chiral condensate is largely reserved. In contrast, the chiral condensate becomes zero by the $xy$-projection in the DR gauge. This indicates that $A_{t}(s)$ and $A_{z}(s)$ play a dominant role, while $A_{x}(s)$ and $A_{y}(s)$ play no role, in spontaneous chiral-symmetry breaking in the DR gauge.

hep-lat↗

arXiv2026

Learning Low Modes of the Wilson Dirac Operator with Gauge-Equivariant Networks

In adaptive multigrid, test vectors that better approximate the low-mode subspace of the Wilson Dirac operator $D$ can reduce the solve time, but their construction can be costly. In some cases, the setup takes longer than a single solve. To reduce the cost of generating test vectors, we train networks built from gauge-equivariant parallel-transport layers once on a quenched ensemble, using a Rayleigh-Ritz loss for $D^\dagger D$. We then test whether the trained networks maintain their performance at other hopping parameters and on configurations not used in training. In these tests, the network outputs are used as test vectors, and the costly $V$-cycle refinement in the adaptive setup is omitted to reduce the setup time. This substantially reduces the setup time while leaving the solve time largely unchanged in most cases. Near the critical hopping parameter $κ_c$, the solve time is also reduced in some cases.

hep-lat↗

arXiv2026

Towards Systematic Control of the Nucleon Gluon PDF with the Pseudo-PDF Method

We present updated lattice quantum chromodynamics (QCD) results for the unpolarized nucleon gluon parton distribution function (PDF) using the pseudo-PDF methodology. The calculation is performed at valence pion masses $M_π\approx 310$ and $690$ MeV on an $a \approx 0.06$ fm ensemble with $2+1+1$ flavors of highly improved staggered quarks (HISQ) generated by the MILC Collaboration. This lattice spacing is finer than those used in previous gluon pseudo-PDF studies, providing access to multiple short-distance separations and nucleon boost momenta as high as $4.4$ GeV. To control excited-state contamination and reduce model dependence, we employ the recently developed Lanczos method, finding good agreement with our previous two-state fit approach. Higher-twist contributions and discretization effects are accounted for through explicit parameterizations in fits to the renormalized short-distance matrix elements. Together, these advances represent important steps toward systematically controlled, high-precision extractions of the gluon PDF. The resulting PDFs exhibit no statistically significant dependence on the valence pion mass and indicate a strongly suppressed gluon distribution at large $x$, consistent with a subset of phenomenological PDF extractions. These results demonstrate progress toward providing systematically controlled lattice-QCD constraints for future global PDF analyses.

hep-lat↗