Non-perturbative definition of the QCD energy-momentum tensor on the lattice

Understand

We present a strategy to define non-perturbatively the energy-momentum tensor in Quantum Chromodynamics (QCD) which satisfies the appropriate Ward identities and has the right trace anomaly.

• The tensor is defined by regularizing the theory on a lattice, and by fixing its renormalization constants non-perturbatively by suitable Ward identities associated to the Poincare' invariance of the continuum theory.
• The latter are derived in thermal QCD with a non-zero imaginary chemical potential formulated in a moving reference frame.
• A renormalization group analysis leads to simple renormalization-group-invariant definitions of the gluonic and fermionic contributions to either the singlet or the non-singlet components of the tensor, and therefore of their form factors among physical states.