Projective invariance and one-loop effective action in affine metric gravity interacting with a scalar field

Abstract

We investigate the influence of the projective invariance on the renormalization properties of the theory. One-loop counterterms are calculated in the most general case of interaction of gravity with scalar field.

On a theorem of de la Harpe and Karoubi

“…In the present paper, we have considered the affine-metric gravity with extra local symmetries (16) related to the transformations of the affine connection. These symmetries do not have an 'ordinary' physical meaning and geometrical nature: for the extra local symmetries no additional gauge fields appear.…”

“…An affine-metric theory of gravity may have additional local symmetries related to transformations of the connection [14][15][16]. The simplest is the transformation of irreducible parts of the connection.…”

“…Consider the question of anomalies, related to transformations (16). An anomaly is a violation of some classical symmetry at the quantum level.…”

“…The transformations (16) and the variation of the affine-metric action do not explicitly depend on the spacetime dimension. Consequently, there is no anomaly in the theory associated with these transformations.…”

“…This theory may be invariant with respect to some extra local transformations of the affine connection for special values of the coefficients [14][15][16]. These invariances restrict arbitrariness of the initial Lagrangian and avoid undesirable counterterms at the quantum level.…”