Metric-Affine Gravity as an effective field theory

The origin of Weyl gauging in metric-affine theories

“…One natural reason to incorporate Weyl symmetry in gravity and metric-affine theories is to try to construct a theory that is "complete" above some ultraviolet scale, which is generally associated with the Planck mass. In fact, metric and metric-affine theories are generally interpreted as effective ones [14], because, among other things, it is not clear if they are predictive at all energy scales, especially if quantum mechanical effects are taken into account. Needless to say, the formalism developed in this paper can also have potentially interesting implications in the context of theories equivalent to general relativity, e.g.…”

“…The motivation for such an approach is that, even though the torsion that is used in this section is Weyl covariant, it is not isomorphic (meaning in one-to-one correspondence) to the contortion tensor, which has an affine Weyl transformation. This feature comes from the torsion-vector contribution stemming from the presence of the Weyl potential in (14). In fact, in the approach of this section the torsion transforms as a Weyl gauge potential, which has allowed for applications in which the torsion vector itself (modulo a constant) plays the role of S µ , see [26][27][28].…”

“…If we take the gauge field of the new Abelian group to be S µ itself, i.e. the Weyl potential, then we can extend ∇ in (14) as…”

“…However, we need not forget that our understanding of general relativity, and of the standard model for what matters, is, now more than ever, leaning towards the fact that they are effective theories [14], that work well on certain intervals of scales, while eluding us outside of them. Assuming that general relativity's metric and connection effective degrees of freedom are also fundamental ones should be regarded as an endeavor, instead of an obvious natural assumption.…”

Coupling Metric-Affine Gravity to a Higgs-Like Scalar Field

“…Note that this is already the case in metric gravity [52], and numerous additional problematic terms arise in the presence of torsion [53][54][55][56][57]. We must mention, however, that certain combinations of curvature-squared contribution only lead to new propagating degrees of freedom that are healthy; see [150,[176][177][178][179][180][181][182][183][184][185][186][187][188][189] for studies in the presence of torsion and [189,190] for extensions to non-metricity. Moreover, it is possible to construct theories with terms that are quadratic in curvature which do not feature at all any additional propagating degrees of freedom [69].…”