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There are currently two singularity-free universal expressions for the topological susceptibility in QCD, one based on the Yang-Mills gradient flow and the other on density-chain correlation functions. While the latter link the susceptibility to the anomalous chiral Ward identities, the gradient flow permits the emergence of the topological sectors in lattice QCD to be understood. Here the two expressions are shown to coincide in the continuum theory, for any number of quark flavours in the range where the theory is asymptotically free.
Using finite size scaling techniques and a renormalization scheme based on the Gradient Flow, we determine non-perturbatively the $beta$-function of the $SU(3)$ Yang-Mills theory for a range of renormalized couplings $bar g^2sim 1-12$. We perform a d
In K.~Hieda, A.~Kasai, H.~Makino, and H.~Suzuki, Prog. Theor. Exp. Phys. textbf{2017}, 063B03 (2017), a properly normalized supercurrent in the four-dimensional (4D) $mathcal{N}=1$ super Yang--Mills theory (SYM) that works within on-mass-shell correl
The spatial distribution of the stress tensor around the quark--anti-quark ($Qbar{Q}$) pair in SU(3) lattice gauge theory is studied. The Yang-Mills gradient flow plays a crucial role to make the stress tensor well-defined and derivable from the nume
Euclidean two-point correlators of the energy-momentum tensor (EMT) in SU(3) gauge theory on the lattice are studied on the basis of the Yang-Mills gradient flow. The entropy density and the specific heat obtained from the two-point correlators are s
We study the spatial distribution of the stress tensor around static quark-anti-quark pair in SU(3) lattice gauge theory. In particular, we reveal the transverse structure of the stress tensor distribution in detail by taking the continuum limit. The