Abstract
The product of gauge fields generated by the Yang-Mills gradient flow for positive flow times does not exhibit the coincidence-point singularity and a local product is thus independent of the regularization. Such a local product can furthermore be expanded by renormalized local operators at zero flow time with finite coefficients that are governed by renormalization group equations. Using these facts, we derive a formula that relates the small flow-time behavior of certain gauge-invariant local products and the correctly-normalized conserved energy-momentum tensor in the Yang-Mills theory. Our formula provides a possible method to compute the correlation functions of a well-defined energy-momentum tensor by using lattice regularization and Monte Carlo simulation.
Highlights
Lattice regularization provides a very powerful non-perturbative formulation of field theories, it is incompatible with fundamental global symmetries quite often
We have derived a formula that relates the short flow-time behavior of some gauge-invariant local products generated by the Yang–Mills gradient flow and the correctly-normalized conserved energy–momentum tensor in the Yang–Mills theory
Si√nce the lattice spacing a must be sufficiently smaller than the square-root of the flow time 8t for our reasoning to work, the reliable application of Eq (4.29) will require rather small lattice spacings
Summary
Lattice regularization provides a very powerful non-perturbative formulation of field theories, it is incompatible with fundamental global symmetries quite often. By using the above properties of the gradient flow, one can obtain a formula that relates the small flow-time behavior of certain gauge-invariant local products and the energy– momentum tensor defined by the dimensional regularization Since the former can be computed by using the Wilson flow with lattice regularization [31,32,33,34,35,36,37,38,39] and the latter is conserved and generates correctly-normalized translations on composite operators, our formula provides a possible method to compute the correlation functions of a correctly-normalized conserved energy–momentum tensor by using Monte Carlo simulation.
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