Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · hep-lat/9808054

Monopoles and Gluon Fields in QCD in the Maximally Abelian Gauge

Hiroko Ichie·Hideo Suganuma
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study monopoles and gluon fields in QCD in the maximally abelian (MA) gauge in the context of the dual superconductor picture for confinement. In the abelian gauge, unit-charge magnetic monopoles appear, but multi-charge monopoles do not in general cases. The appearance of the monopole is studied using the gauge-connection formalism in relation to the SU($N_c$) singular gauge transformation. The relevant role of off-diagonal gluons is found for the appearance of monopoles in the abelian gauge in QCD. We study the gluon-field properties around the monopole in the MA gauge in terms of the action density using the lattice QCD. The monopole provides infinitely large field fluctuations in the abelian sector. In the MA gauge, off-diagonal gluons are strongly suppressed but largely remain around the monopole, which indicates the effective size and the structure of monopoles. We find the large cancellation between the abelian part and the off-diagonal part of the action density around the monopole in the MA gauge. Owing to this cancellation, the monopole can appear in QCD without large cost of the QCD action. Finally, we generalize the framework of the abelian projection, {\it i.e.} the extraction of the abelian gauge manifold from QCD, by introducing the `gluonic Higgs field' $\vec ϕ_D[A_μ(x)]$ defined from the ${\rm SU}(N_c)$ covariant derivative $\hat D_μ$. By way of $\vec ϕ_D[A_μ(x)]$, the maximally abelian projection can be performed in the gauge-covariant manner without the notion of gauge fixing in principle.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hiroko Ichie, Hideo Suganuma. 1998-08-29. Monopoles and Gluon Fields in QCD in the Maximally Abelian Gauge. https://doi.org/10.1016/s0550-3213(99)00758-0

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

KEEP EXPLORING

Related papers

arXiv2026

Measuring Mass Splittings in Baryon SU(2) Multiplets

The inclusion of isospin-breaking corrections arising from electromagnetic interactions and the up-down quark mass difference is becoming increasingly important in lattice QCD calculations, as the precision of observables is at or approaching the percent level. In this context, the RM123 method has been employed in recent years to take into account such isospin corrections. In this work, we study baryon mass splittings using the RM123 approach. Preliminary results are presented for the mass splittings within spin-1/2 and spin-3/2 baryon SU(2) multiplets, obtained using twisted-mass ensembles tuned close to physical quark masses. We consider only valence contributions, with the splittings computed at leading order in the isospin-breaking parameters.

hep-lat↗
arXiv2026

The Peskin-Takeuchi $S$ parameter and vector meson decay constants in $N_f=8$ QCD

We use lattice gauge theory to investigate the Peskin-Takeuchi S parameter in SU(3) gauge theory with eight light fundamental fermions (eight-flavor QCD), a candidate for walking technicolor. We develop a new approach to computing S using the first time moment of current correlators, in addition to the conventional vacuum-polarization method, and obtain consistent results. Finite-volume (FV) corrections are estimated using data at multiple lattice volumes and a formula motivated by chiral perturbation theory. At the smallest fermion mass, the one-doublet contribution is S = 0.281(5)(17), smaller than the value $\sim 0.35$ in scaled-up 2+1-flavor QCD (without subtracting the SM contribution). However, contrary to naive expectations, S toward smaller fermion masses is not necessarily suppressed once FV corrections are included. The resulting Gasser-Leutwyler parameter $L_{10}^r(M_ρ)$ is similar to that in real-world QCD. We also determine the vector and axial-vector meson decay constants, $F_ρ$ and $F_{a_1}$. The ratio $F_ρ/F_π$ is stable against the fermion mass and consistent with the KSRF estimate, implying a $ρππ$ coupling similar to that in real-world QCD. We predict the techni-rho decay width into weak bosons to be $Γ_ρ/M_ρ\lesssim 0.24/N$, where N is the number of weak doublets. We further find that the rho- and $a_1$-dominated Weinberg spectral-function and Das-Mathur-Okubo sum rules are satisfied, yielding S and $L_{10}^r(M_ρ)$ consistent with our main results. We discuss implications for BSM model building.

hep-lat↗
arXiv2026

Multilevel Plaquette-Space Sampling for Lattice Gauge Theories with Local Constraint Solves

Lattice gauge theories are an important class of physical models with high-dimensional structured distributions that underpin first-principles calculations in particle, nuclear, and condensed-matter physics. Recent advances in generative modeling have opened new avenues for sampling Boltzmann distributions in lattice gauge theories, offering the potential to alleviate limitations of traditional Monte Carlo methods, including critical slowing down and topological freezing. However, generative samplers for lattice gauge theories are typically constructed in link space, where correlations become increasingly long-ranged toward weak coupling, posing a challenge for learning. Plaquettes provide a more natural representation, as the action is local in these variables. However, exact Bianchi constraints restrict them to a lower-dimensional manifold, complicating direct generative modeling. We introduce a multilevel normalizing-flow construction that samples directly in plaquette space while satisfying these constraints exactly. The key idea is a coarse-to fine factorization that transforms a globally coupled constraint problem into a sequence of local solves: at each refinement, every determined plaquette depends on at most four newly generated variables, while the size of the constraint problem remains independent of the lattice size. We validate the construction for $U(1)$ in two and four dimensions and for $SU(2)$ in two dimensions. Our multilevel Plaquette-Space Sampler (PSS) substantially outperforms link-space baselines, with the advantage increasing toward weak coupling, where the gauge coupling becomes small. This regime is particularly challenging for generative sampling and, in asymptotically free gauge theories, is relevant to continuum studies.

hep-lat↗