arXiv subjects

Públio Rwany B. R. do Vale

Publications and source records attributed to Públio Rwany B. R. do Vale.

4 recordsLinked to original sources

arXiv2026

Conformal anomaly in a vector field model with auxiliary scalar field

The conformal anomaly has well-known ambiguities related to the possible schemes of regularization and renormalization. In case of dimensional regularization, one of the options is to formulate the theory as conformal in the dimension $D \neq 4$. For a gauge vector field this can be done in several ways and one of the options is to introduce an auxiliary scalar playing the role of a compensator. The advantage of this approach is that it preserves gauge symmetry and avoids problems with possible violation of unitarity. We explore the consequences of introducing such an auxiliary field for the anomaly and anomaly-induced action. It is shown that the new scalar degree of freedom gains an independent dynamics after taking the $4D$ limit. The remnant scalar, also, demonstrates some interesting properties.

hep-th↗

arXiv2026

Conditions for positivity of energy in superrenormalizable polynomial gravity

At the quantum level, the polynomial models of gravity with six and eight derivatives are superrenormalizable, but suffer from higher derivative ghost and/or tachyonic ghost states. On the other hand, these models may have advantages in the control of negative effects of ghosts, compared to the more common fourth-derivative theory. We explore the positiveness of energy of the individual plane wave solutions in the general models with six and eight derivatives. Different from the fourth-order gravity, the part of the energy which may be seen as the leading one in the UV, is positively defined in the tensor sector. We extend this investigation to the scalar sectors of the free theory.

gr-qc↗

arXiv2024

On the renormalization of massive vector field theory coupled to scalar in curved space-time

We consider the renormalization of massive vector field interacting with charged scalar field in curved spacetime. Starting with the theory minimally coupled to external gravity and using the formulations with and without Stückelberg fields, we show that the longitudinal mode of vector field is completely decoupled and the remaining theory of transverse vector field is renormalizable by power counting. The formal arguments based on the covariance and power counting indicate that multiplicative renormalizability of the interacting theory may require introducing two non-minimal terms linear in Ricci tensor in the vector sector. Nevertheless, a more detailed analysis shows that these non-minimal terms violate the decoupling of the longitudinal mode and are prohibited. As a verification of general arguments, we derive the one-loop divergences in the minimal massive scalar QED, using Stückelberg procedure and the heat-kernel technique. The theory without non-minimal terms proves one-loop renormalizable and admits the renormalization group equations for all the running parameters in the scalar and vector sectors. One-loop beta functions do not depend on the gauge fixing and can be used to derive the effective potential.

hep-th↗

arXiv2024

Generalization of conformal Hamada operators

The six-derivative conformal scalar operator was originally found by Hamada in its critical dimension of spacetime, $d=6$. We generalize this construction to arbitrary dimensions $d$ by adding new terms cubic in gravitational curvatures and by changing its coefficients of expansion in various curvature terms. The consequences of global scale-invariance and of infinitesimal local conformal transformations are derived for the form of this generalized operator. The system of linear equations for coefficients is solved giving explicitly the conformal Hamada operator in any $d$. Some singularities in construction for dimensions $d=2$ and $d=4$ are noticed. We also prove a general theorem that a scalar conformal operator with $n$ derivatives in $d=n-2$ dimensions is impossible to construct. Finally, we compare our explicit construction with the one that uses conformal covariant derivatives and conformal curvature tensors. We present new results for operators built with different orders of conformal covariant derivatives.

hep-th↗