Disorder parameter for confinement and vacuum field strength correlators

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

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

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).

hep-lat↗