Erratum to: The two-loop energy–momentum tensor within the gradient-flow formalism

Abstract

Two typos in Ref. 1 are corrected.

Gradient Flow: Perturbative and Non-Perturbative Renormalization

“…where ζ χ has been determined at 1-loop in [46,47] and up to 2-loops in Refs. [13,57]. The calculation of the matching coefficients can be summarized with the following steps.…”

“…[69] with a 2-loop matching, using the perturbative calculation of Ref. [57]. A different approach has been proposed in Ref.…”

QCD static force in gradient flow

“…The gradient-flow formulation has been proved useful in lattice QCD calculations of correlation functions and local operator matrix elements [23][24][25][26][27][28][29][30][31]. In gradient flow, the gauge fields in the operator definitions of matrix elements are replaced by flowed fields that depend on the spacetime coordinate and the flow time t. At tree level in perturbation theory, the flowed fields come with a factor e −q 2 t for every momentum-space gauge field with momentum q in the operator definition, which gives an exponential suppression factor at large q in the Fourier transformation.…”

The gradient flow at higher orders in perturbation theory

“…The coefficients 𝑐 𝑛 (𝑡) are finite even without operator renormalization. They have been evaluated through NNLO [29,30,37] and used to study thermodynamics of QCD [32,[38][39][40][41].…”