André Lehum
Institute of Exact and Natural Sciences
Federal University of Pará - Belém - Brazil

New paper investigates how quantum gravity affects the running of the electric charge

I am pleased to share that my paper, written in collaboration with M. Gomes and A. J. da Silva, entitled On the physical running of the electric charge in a dimensionless theory of gravity, has been accepted for publication in Physical Review D.

In this work, we address an important conceptual issue at the interface between quantum field theory and perturbative quantum gravity: how to properly define the running of the electric charge when massless quantum electrodynamics is coupled to a dimensionless quadratic theory of gravity. In physical terms, the central question is whether gravitational effects modify the way the strength of the electromagnetic interaction evolves with energy scale.

Our main result is that at one loop, quadratic gravity does not modify the beta function of the electric charge. We show that, in this setting, it is crucial to distinguish carefully between ultraviolet logarithmic contributions, which govern renormalization and the genuine running of the coupling, and infrared logarithmic contributions, associated with soft and nonlocal effects, which should not be interpreted as physical corrections to the ultraviolet evolution of the charge.

This result helps clarify an ambiguity that has appeared in recent discussions in the literature concerning the difference between the standard renormalization-group running and a supposed “physical running” extracted directly from the logarithmic dependence of amplitudes on the external momentum. The paper shows that, once infrared effects are properly treated, these two notions coincide in one-loop quantum electrodynamics, even in the presence of quadratic gravity.

Beyond its technical interest, the paper also contributes to a broader question: the consistent identification of physical observables in higher-derivative gravitational theories. This is a relevant issue in renormalizable approaches to quantum gravity, where improved ultraviolet behavior comes together with conceptual subtleties involving gauge choice, unitarity, and the interpretation of radiative effects.

The paper is available on arXiv: On the physical running of the electric charge in a dimensionless theory of gravity, e-Print: 2512.11742 [hep-th].
DOI: https://doi.org/10.1103/gc68-584n

Testing Quantum Gravity in Quark and Gluon Collisions Beyond the Planck Scale

The article “Ultra-Planckian Quark and Gluon Scattering in Agravity”, developed by Ivana F. Cunha and André C. Lehum from the Faculty of Physics at UFPA, has just been accepted for publication in the journal Physical Review D.

What is this research about?

This work investigates how scale-free quantum gravity, known as Agravity, behaves in high-energy collisions of quarks and gluons at energies surpassing the Planck scale, the threshold where quantum gravitational effects become significant.

Why does it matter?

While Einstein's theory of gravity has been remarkably successful, it cannot be quantized in a renormalizable way like the other fundamental forces. Agravity, by incorporating quadratic curvature terms, offers a renormalizable and scale-free quantum theory of gravity, allowing the Planck scale to emerge dynamically.

Testing this theory in scattering processes involving fundamental particles is crucial to assess its consistency, unitarity (physically meaningful probabilities), and behavior at extreme energy scales.

What did we do?

For the first time within the Agravity framework, we explicitly calculated the gravitational scattering amplitudes for:

• Gluon-gluon → gluon-gluon (gg → gg)

• Gluon-gluon → quark-antiquark (gg → qq̄)

• Gluon-quark → gluon-quark (gq → gq)

• Quark-quark → quark-quark (qq → qq)

focusing on the ultra-high-energy regime and isolating purely gravitational effects in these interactions.

Key findings

• The cross sections decrease as 1/E² at high energies, consistent with expectations for a well-behaved quantum theory of gravity.

• The squared amplitudes remain positive over a wide angular range, ensuring unitarity even in the presence of the “ghost” modes typical in higher-derivative gravity theories.

• Quark masses act as natural infrared regulators, removing divergences at small angles and ensuring physically meaningful results.

• We confirmed the compatibility between unitarity and ultraviolet (UV) completeness in Agravity, supporting its viability as a quantum extension of gravity.

Why is this relevant to high energy physics?

This work advances our understanding of UV-complete quantum gravity theories, demonstrating that Agravity retains consistent physical properties even at energies beyond the Planck scale—an important scenario for unification theories and early-universe cosmology.

Moreover, it contributes to the ongoing exploration of how gravitons interact with quarks and gluons at ultra-high energies, a regime beyond current experimental reach but fundamental for guiding the future of quantum gravity research.

Reference: I. F. Cunha and A. C. Lehum, "Ultra-Planckian Quark and Gluon Scattering in Agravity," [arXiv:2505.19957 [hep-th]].

Dynamical Lorentz symmetry breaking and the origin of 𝐺: A speculative perspective

I am thrilled to announce the acceptance of our article, titled "Dynamical Lorentz symmetry breaking in a scale-free theory of gravity," for publication in Physical Review D. This work, conducted in collaboration with J. R. Nascimento, A. Yu. Petrov, and P. J. Porfírio, explores a fascinating connection between scale-free gravity and the phenomenon of dynamical Lorentz symmetry breaking.

In this study, we investigate the renormalization of scale-free quadratic gravity coupled to the bumblebee field, a model theoretically motivated for its ability to spontaneously break Lorentz symmetry. We performed the one-loop renormalization of the model and calculated the associated renormalization group functions. Furthermore, we computed the one-loop effective potential for the bumblebee field, demonstrating that it acquires a non-trivial vacuum expectation value (VEV) through radiative corrections, a phenomenon known as the Coleman-Weinberg mechanism.

Remarkably, we showed that this spontaneous breaking of scale invariance, induced by the VEV of the bumblebee field, leads to Lorentz symmetry violation. In a speculative scenario, we argue that the non-minimal coupling between the bumblebee and gravitational fields can spontaneously generate the Einstein-Hilbert term via radiative corrections. This suggests an intriguing possibility: Newton’s gravitational constant (𝐺) could be deeply connected to the dynamical breaking of Lorentz and scale invariances.

Our work opens new perspectives on how quantum gravity and Lorentz symmetry may be interconnected, providing theoretical insights into the origin of fundamental scales in physics.

Reference: A. C. Lehum, J. R. Nascimento, A. Yu. Petrov, and P. J. Porfírio, "Dynamical Lorentz symmetry breaking in a scale-free theory of gravity," Phys. Rev. D 110, 125007 (2024).

The preprint of this work is available on ArXiv: https://arxiv.org/abs/2406.08309.

Exploring gravitational corrections in non-Abelian gauge theories

I am pleased to share the publication of our latest work in Physical Review D. In collaboration with M. Gomes and A. J. da Silva, we investigate how massive fermions interact with gravity within the framework of a non-Abelian gauge theory. Using effective field theory for quantum gravity, we performed detailed calculations of the two-loop beta function for the gauge coupling constant, employing the one-graviton exchange approximation.

One of the most important properties of non-Abelian gauge theories is asymptotic freedom. Discovered by David Gross and Frank Wilczek, and independently by David Politzer in 1973, this phenomenon entails a decrease in the strength of the gauge coupling constant as energy scales increase. This attribute is crucial when employing non-Abelian gauge theories to describe strong interactions. Our work builds on this principle by investigating how gravitational corrections influence the behavior of the coupling constant at high energy scales.

Our findings reveal that gravitational corrections can, under certain conditions, lead to a non-trivial ultraviolet (UV) fixed point in the beta function of the gauge coupling constant. For Quantum Chromodynamics (QCD) with 6 fermions, our calculations show that the UV fixed point would require a much larger mass than that of the top quark, making it unfeasible under current conditions. However, in speculative scenarios, such as those suggested by Kaluza-Klein models, a UV fixed point could emerge if additional fermions are introduced.

These results open new avenues for discussions on how gravity might influence gauge coupling dynamics across various theories.

The paper was published as: 

• M. Gomes, A. C. Lehum e A. J. da Silva, "Gravitational corrections to the two-loop beta function in a non-Abelian gauge theory," Phys. Rev. D 110, 065007 (2024), doi:10.1103/PhysRevD.110.065007, [arXiv:2408.02512 [hep-th]].

Advances in the study of Lorentz symmetry violations in field theories

In recent years, my research has focused on studying Lorentz symmetry violations in quantum field theories. Recently, I published two papers that explore quantum corrections in different variants of Lorentz-violating quantum electrodynamics (QED), in collaboration with researchers from various institutions.

• Two-Loop Corrections to the Carroll-Field-Jackiw Term in CPT-Odd Scalar QED

In the paper titled "Two-loop corrections to the Carroll-Field-Jackiw term in a CPT-odd Lorentz-violating scalar QED," published in Physics Letters B, co-authored with J. R. Nascimento and A. Yu. Petrov, we investigated scalar QED with CPT-odd Lorentz violation. Our focus was on calculating one- and two-loop corrections to Lorentz-violating vertices, as well as determining the finite two-loop corrections to the Carroll-Field-Jackiw (CFJ) term, which is essential for understanding how these violations manifest in quantum theories.

One of the main conclusions of the work was demonstrating that the CFJ term remains finite at two-loop corrections without requiring a nontrivial vacuum, resolving ambiguities often encountered in theories involving fermions. This result is an important advancement in understanding Lorentz-violating theories, especially in the presence of a scalar vacuum, and opens the door to further studies at higher perturbative orders.

Reference:

A. C. Lehum, J. R. Nascimento and A. Yu. Petrov, "Two-loop corrections to the Carroll-Field-Jackiw term in a CPT-odd Lorentz-violating scalar QED," Phys. Lett. B 850, 138519 (2024). DOI: 10.1016/j.physletb.2024.138519 [arXiv:2310.15715 [hep-th]].

• Two-Loop Renormalization in CPT-Even Scalar QED

Another study was published in the paper "Two-loop renormalization of the CPT-even Lorentz-violating scalar QED," co-authored with L. C. T. Brito, J. C. C. Felipe, and A. Yu. Petrov, in the European Physical Journal Plus. This work presents a detailed analysis of the two-loop renormalization in CPT-even Lorentz-violating scalar QED, focusing on quantum effects in two- and three-point functions within the context of high-loop perturbative theory.

Using advanced computational tools, we calculated the beta functions and verified the consistency of the Ward identities, confirming the consistency of the theory. This is the first explicit calculation of a two-loop correction in a Lorentz-violating field theory model, opening new possibilities for future studies, such as applying these methods to other Lorentz-violating field theories, including CPT-odd scalar QED and scalar QCD.

Reference:

L. C. T. Brito, J. C. C. Felipe, A. C. Lehum and A. Yu. Petrov, "Two-loop renormalization of the CPT-even Lorentz-violating scalar QED," Eur. Phys. J. Plus 139, 90 (2024). DOI: 10.1140/epjp/s13360-024-04891-z [arXiv:2306.08488 [hep-th]].

These works mark some advances in the study of Lorentz symmetry violations in quantum field theories, with both theoretical and phenomenological implications. We will continue to explore this fascinating field, aiming to deepen our understanding of quantum effects and their potential experimental detection.

New articles published in Physical Review D

Good news as 2021 comes to a close! We had two articles published in the prestigious journal Physical Review D, both with the participation of Huan Souza, a master's student under my supervision.

In the article titled 'Gravitational corrections to the two-loop beta function in quantum electrodynamics', we used the effective field theory approach to couple Einstein's theory of gravity to quantum electrodynamics and determine subleading-order corrections to the beta function of the electric charge. Our results indicate that, contrary to what was suggested by Robinson and Wilczek, gravitational corrections do not make the electric charge asymptotically free. In fact, these corrections contribute to the charge growing even faster. This work was carried out in collaboration with researchers L. Beviláqua (UFRN), M. Dias, and C. Senise (UNIFESP), A. J. da Silva (USP), and H. Souza (UFPA).

In the second article, titled 'Universality of the gauge coupling constant in the Einstein-QED system', we discuss how the renormalization of the electric charge can be defined universally, that is, independently of the process. We showed that although the renormalization of the fermion-photon interaction vertices depends on the generation of the involved fermion, the Ward identity (a manifestation of gauge symmetry) ensures that the renormalized electric charge is process-independent. This work was done in collaboration with researchers L. Beviláqua (UFRN) and H. Souza (UFPA).

To learn more, visit the links to the articles on the PRD server or the ArXiv preprint site

1. Gravitational corrections to two-loop beta function in quantum electrodynamics (PRD, ArXiv);

2.  Universality of gauge coupling constant in the Einstein-QED system (PRD, ArXiv).

Perturbative aspects of mass-deformed N=3 Chern-Simons-matter theory in Physical Review D

In the article titled 'Perturbative aspects of mass-deformed N=3 Chern-Simons-matter theory', recently published in the specialized journal Physical Review D, we discuss some quantum aspects of this theory. Chern-Simons theories are widely applied in the description of condensed matter systems, such as the phenomenon of superconductivity, and their supersymmetric versions are closely related to certain solutions in String Theory, known as M2-branes. The work was carried out in collaboration with researchers Albert Petrov and José Roberto do Nascimento, both from the Federal University of Paraíba. To learn more, visit the article's page on the PRD server or the ArXiv preprint site.