Motivated by the search for possible CP violating terms in the trace of the energy-momentum tensor in theories coupled to gravity we revisit the problem of trace anomalies in chiral theories. We recalculate the latter and ascertain that in the trace of the energy-momentum tensor of theories with chiral fermions at one-loop the Pontryagin density appears with an imaginary coefficient. We argue that this may break unitarity, in which case the trace anomaly has to be used as a selective criterion for theories, analogous to the chiral anomalies in gauge theories. We analyze some remarkable consequences of this fact, that seem to have been overlooked in the literature.

We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local and weakly nonlocal gravitational theories that are quadratic in both, the Ricci and scalar curvature with form factors of the d’Alembertian operator inserted between. More specifically we are interested in renormalizable, super-renormalizable or finite theories. The scattering amplitudes for these theories turn out to be the same as the ones of Einstein gravity regardless of the explicit form of the form factors. As a special case the four-graviton scattering amplitudes in Weyl conformal gravity are identically zero. Using a field redefinition, we prove that the outcome is correct for any number of external gravitons (on-shell n−point functions) and in any dimension for a large class of theories. However, when an operator quadratic in the Riemann tensor is added in any dimension (with the exception of the Gauss-Bonnet term in four dimensions) the result is completely altered, and the scattering amplitudes depend on all the form factors introduced in the action.

This article deals with two main topics. One is odd parity trace anomalies in Weyl fermion theories in a 4d curved background, the second is the introduction of axial gravity. The motivation for reconsidering the former is to clarify the theoretical background underlying the approach and complete the calculation of the anomaly. The reference is in particular to the difference between Weyl and massless Majorana fermions and to the possible contributions from tadpole and seagull terms in the Feynman diagram approach. A first, basic, result of this paper is that a more thorough treatment, taking account of such additional terms and using dimensional regularization, confirms the earlier result. The introduction of an axial symmetric tensor besides the usual gravitational metric is instrumental to a different derivation of the same result using Dirac fermions, which are coupled not only to the usual metric but also to the additional axial tensor. The action of Majorana and Weyl fermions can be obtained in two different limits of such a general configuration. The results obtained in this way confirm the previously obtained ones.

In a theory of a Dirac fermion field coupled to a metric-axial-tensor (MAT) background, using a Schwinger-DeWitt heat kernel technique, we compute non-perturbatively the two (odd parity) trace...

In quantum field theory, an orbifold is a way to obtain a new theory from an old one by gauging a finite global symmetry. This definition of orbifold does not make sense for quantum gravity theories, that admit (conjecturally) no global symmetries. In string theory, the orbifold procedure involves the gauging of a global symmetry on the world-sheet theory describing the fundamental string. Alternatively, it is a way to obtain a new string background from an old one by quotienting some isometry.We propose a new formulation of string orbifolds in terms of the group of gauge symmetries of a given string model. In such a formulation, the ‘parent’ and the ‘child’ theories correspond to different ways of breaking or gauging all potential global symmetries of their common subsector. Through a couple of simple examples, we describe how the higher group structure of the gauge group in the parent theory plays a crucial role in determining the gauge group and the twisted sector of the orbifold theory. We also discuss the dependence of this orbifold procedure on the duality frame.