On the geometric origin of the energy-momentum tensor improvement terms

In a flat background, the canonical energy momentum tensor of Lorentz and conformally invariant matter field theories can be improved to a symmetric and traceless tensor that gives the same conserved charges. We argue that the geometric origin of this improvement process is unveiled when the matter theory is coupled to Metric-Affine Gravity. In particular, we show that the Belinfante-Rosenfeld improvement terms correspond to the matter theory's hypermomentum. The improvement terms in conformally invariant matter theories are also related to the hypermomentum however a general proof would require an extended investigation. We demonstrate our results through various examples, such as the free massless scalar, the Maxwell field, Abelian $p$-forms, the Dirac field and a non-unitary massless scalar field. Possible applications of our method for theories that break Lorentz or special conformal invariance are briefly discussed.