Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory

Abstract

We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward Identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincare` invariance of the continuum theory. These relations come forth when the length of the box in the temporal direction is finite, and they take a particularly simple form if the coordinate and the periodicity axes are not aligned. We implement the method for the SU(3) Yang--Mills theory discretized with the standard Wilson action in presence of shifted boundary conditions in the (short) temporal direction. By carrying out extensive numerical simulations, the renormalization constants of the traceless components of the tensor are determined with a precision of roughly half a percent for values of the bare coupling constant in the range 0<= g^2_0<=1.

arXiv comment22 pages, 6 figures. Minor typos corrected. Version accepted for publication on PRD

References in corpus (9)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• A study of the 't Hooft loop in SU(2) Yang-Mills theory
• Lattice energy-momentum tensor from the Yang-Mills gradient flow -- inclusion of fermion fields
• Space-time symmetries and the Yang-Mills gradient flow
• Thermal momentum distribution from path integrals with shifted boundary conditions
• Implications of Poincare symmetry for thermal field theories in finite-volume
• Thermodynamic potentials from shifted boundary conditions: the scalar-field theory case
• Equation of state of a relativistic theory from a moving frame
• A novel approach for computing glueball masses and matrix elements in Yang-Mills theories on the lattice

Cited by in corpus (18)

• Low-energy effective action for pions and a dilatonic meson
• Equation of state of the SU($3$) Yang-Mills theory: a precise determination from a moving frame
• Quantum algorithms for transport coefficients in gauge theories
• Inhomogeneity of rotating gluon plasma and Tolman-Ehrenfest law in imaginary time: lattice results for fast imaginary rotation
• Correlations of Energy-Momentum Tensor via Gradient Flow in SU(3) Yang-Mills Theory at Finite Temperature
• Thermodynamics in quenched QCD: energy--momentum tensor with two-loop order coefficients in the gradient flow formalism
• Proof of the renormalizability of the gradient flow
• Viscosity of pure-glue QCD from the lattice
• Frontiers of finite temperature lattice QCD
• Themodynamics for pure SU($2$) gauge theory using gradient flow
• Two-loop renormalization and mixing of gluon and quark energy-momentum tensor operators
• Renormalization of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow
• Non-perturbative renormalization of the QCD flavour-singlet local vector current
• Energy-momentum tensor in QCD: nucleon mass decomposition and mechanical equilibrium
• Shear and bulk viscosities of the gluon plasma across the transition temperature from lattice QCD
• High statistics lattice study of stress tensor correlators in pure $SU(3)$ gauge theory
• From Special Relativity to embedded generators in Cartan subalgebras of rank-4 spin algebras
• The energy-momentum tensor in lattice QCD and the Equation of State