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Register a new userRenormalisation of the scalar energy-momentum tensor with the Wilson flow
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The non-perturbative computation of the energy-momentum tensor can be used to study the scaling behaviour of strongly coupled quantum field theories. The Wilson flow is an essential tool to find a meaningful formulation of the energy-momentum tensor on the lattice. We extend recent studies of the renormalisation of the energy-momentum tensor in four-dimensional gauge theory to the case of a three-dimensional scalar theory to investigate its intrinsic structure and numerical feasibility on a more basic level. In this paper, we discuss translation Ward identities, introduce the Wilson flow for scalar theory, and present our results for the renormalisation constants of the scalar energy-momentum tensor.
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A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of $SU(N)$ with a $varphi^4$ interaction on the lattice. In this theory the energy-momentum tensor can mix with $varphi^2$ and we present numerical results for the mixing coefficient for the $N=2$ theory.
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We employ a new strategy for a non perturbative determination of the renormalized energy momentum tensor. The strategy is based on the definition of suitable lattice Ward identities probed by observables computed along the gradient flow. The new set of identities exhibits many interesting qualities, arising from the UV finiteness of flowed composite operators. In this paper we show how this method can be used to non perturbatively renormalize the energy momentum tensor for a SU(3) Yang-Mills theory, and report our numerical results.
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Recently, Harlander et al. [Eur. Phys. J. C {bf 78}, 944 (2018)] have computed the two-loop order (i.e., NNLO) coefficients in the gradient-flow representation of the energy--momentum tensor (EMT) in vector-like gauge theories. In this paper, we study the effect of the two-loop order corrections (and the three-loop order correction for the trace part of the EMT, which is available through the trace anomaly) on the lattice computation of thermodynamic quantities in quenched QCD. The use of the two-loop order coefficients generally reduces the $t$~dependence of the expectation values of the EMT in the gradient-flow representation, where $t$~is the flow time. With the use of the two-loop order coefficients, therefore, the $tto0$ extrapolation becomes less sensitive to the fit function, the fit range, and the choice of the renormalization scale; the systematic error associated with these factors is considerably reduced.
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