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

Understand

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.