Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2411.14812

Lattice gradient flows (de-)stabilizing topological sectors

Yuya Tanizaki·Akio Tomiya·Hiromasa Watanabe
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the stability of topological charge under gradient flow taking the admissibility condition into account. For the $SU(2)$ Wilson gauge theory with $β=2.45$ and $L^4=12^4$, we numerically show that the gradient flows with the Iwasaki and DBW2 gauge actions stabilize the topological sectors significantly, and they have qualitatively different behaviors compared with the Wilson and tree-level Symanzik flows. By considering the classical continuum limit of the flow actions, we discuss that the coefficient of dimension-$6$ operators has to be positive for stabilizing the one-instanton configuration, and the Iwasaki and DBW2 actions satisfy this criterion while the Wilson and Symanzik actions do not. Moreover, we observe that the DBW2 flow stabilizes the topological sectors at the very early stage of the flow ($\hat{t}\approx 0.5$--$1$), suggesting that a further systematic investigation of the DBW2 flow is warranted to confirm its computational efficiency in determining the gauge topology.

Explore related subjects

hep-lathep-thnucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yuya Tanizaki, Akio Tomiya, Hiromasa Watanabe. 2025-03-20. Lattice gradient flows (de-)stabilizing topological sectors. https://arxiv.org/abs/2411.14812

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

KEEP EXPLORING

Related papers

arXiv2026

Flowed quark field renormalization in lattice QCD: A Ward-identity approach and its validation using quark bilinears

We present a non-perturbative Ward-identity prescription for determining the flowed quark field renormalization factor $Z_χ$, avoiding the computational difficulties of the conventional ringed prescription. The method is based on vector-current normalization and ratios of flowed and unflowed meson two-point functions. We determine the resulting $\mathring{Z}_χ^{V}(t_f,a)$ on five $2+1$-flavor clover ensembles and validate it in the pseudoscalar, scalar, axial-vector, and tensor channels. Renormalized matrix elements obtained through sequential continuum and zero-flow-time extrapolations agree with independent RI/MOM and RI/SMOM determinations. The finite-lattice-spacing bilinear renormalization factors show differences that decrease toward finer lattices, reflecting the different discretization effects of the renormalization methods. The cross-channel agreement demonstrates the viability of the proposed prescription; together, the method and its systematic validation establish a robust foundation for the non-perturbative renormalization of flowed fermionic operators in future lattice calculations.

hep-lat↗
arXiv2026

A Guide to Symmetric Mass Generation in Lattice-QCD

Symmetric mass generation (SMG) has attracted growing interest in both condensed matter theory and lattice-QCD communities. Here we formulate general criteria for SMG and examine their compatibility with lattice-QCD. We propose possible RG-flow scenarios near the SMG transition, and argue that meson mass ratio can serve as a probe of the SMG transition viewed as a UV fixed point. We further identify Goldstone tetraquark meson states as phenomenological signatures of the "type-II'' SMG phase.

hep-lat↗
arXiv2026

First-Principles Determination of the QCD Contribution to the Axion-Photon Coupling Using Domain-Wall Fermions

The axion-photon coupling, crucial for experimental axion searches and tests of the strong CP solution, receives a substantial model-independent contribution $\mathcal C_{\rm QCD}$ from QCD dynamics. Next-to-leading-order chiral perturbation theory (NLO ChPT) in different frameworks has yielded puzzling discrepancies of up to $8\%$, motivating precise first-principles calculations. We present an independent lattice QCD determination using a method complementary to the recent background-field calculation. Computing pseudoscalar-to-two-photon three-point functions and exploiting anomalous Ward identities, we separate $\mathcal C_{\rm QCD}$ into an exact anomaly contribution and a light-quark-mass-suppressed correction. The latter is computed using domain-wall fermions, whose excellent chiral symmetry strongly suppresses discretization effects. Working on two near-physical $N_f=2+1$ ensembles with continuum extrapolation, we obtain $\mathcal C_{\rm QCD}^{\rm IS}=1.619(30)$ (isospin-symmetric), $\mathcal C_{\rm QCD}^{\rm IB}=0.347(22)$ (isospin-breaking), and $\mathcal C_{\rm QCD}=1.965(35)$ in total. While direct comparisons with published NLO ChPT predictions reveal apparent tensions, we identify their sources and show that the ChPT results can be reconciled with our lattice determination. Our result provides a first-principles benchmark for the QCD contribution to the axion-photon coupling and a quantitative test of competing ChPT descriptions.

hep-lat↗