Construction of Improved Stress-Energy Tensor in d $ 2

Abstract

The weakest set of necessary and sufficientconditions for the existence of a conserved tracelesssymmetric stress-energy tensor for a scale-invariantPoincare field theory over a d-dimensional flatspace-time manifold has been proved. This improved tensoris explicitly constructed for arbitrary space-timedimensions including d = 2. The example of a vectorfield in d ≥ 3, d ≠ 4 demonstrates that fullconformal symmetry over a flat space-time is sufficientbut not necessary for the existence of an improvedtensor.