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A. C. Lehum

Publications and source records attributed to A. C. Lehum.

At least 37 records · Page 2Linked to original sources
arXiv2023

Gravitational corrections to the Einstein-Scalar-QCD model

This study employs the effective field theory approach to quantum gravity to investigate a non-Abelian gauge theory involving scalar particles coupled to gravity. The study demonstrates explicitly that the Slavnov-Taylor identities are maintained at one-loop order, which indicates that the universality of the color charge is preserved. Additionally, the graviton corrections to the two-loop gluon self-energy and its renormalization are computed.

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arXiv2023

On-shell supersymmetry breaking in the Abelian Chern-Simons-matter model in three dimensions of spacetime

This study examines on-shell supersymmetry breaking in the Abelian $\mathcal{N}=1$ Chern-Simons-matter model within a three-dimensional spacetime. The classical Lagrangian is scale-invariant, but two-loop radiative corrections to the effective potential break this symmetry, along with gauge and on-shell supersymmetry. To investigate this issue, the Renormalization Group Equation is used to calculate the two-loop effective potential.

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arXiv2023

Improved effective potential of Gildener-Weinberg models

The Gildener-Weinberg models are of particular interest in the context of extensions to the Standard Model of particle physics. These extensions may encompass a variety of theories, including double Higgs models, Grand Unification Theories, and proposals for Dark Matter, among others. In order to rigorously test these models experimentally, obtaining precise results is of crucial importance. In this study, we employ the renormalization group equation and its one-loop functions to obtain a deeper understanding of the higher-loop effective potential. Our findings reveal that the radiatively generated mass of the light particle in the Gildener-Weinberg approach experiences a substantial correction. Furthermore, our results suggest that not all flat directions are equivalent and some may be preferred by nature.

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arXiv2023

Three- and Four-Point Functions in CPT-Even Lorentz-Violating Scalar QED

The renormalization of quantum field theories usually assumes Lorentz and gauge symmetries, besides the general restrictions imposed by unitarity and causality. However, the set of renormalizable theories can be enlarged by relaxing some of these assumptions. In this work, we consider the particular case of a CPT-preserving but Lorentz-breaking extension of scalar QED. For this theory, we calculate the one-loop radiative corrections to the three- and four-point scalar-vector vertex functions, at the lowest order in the Lorentz violation parameters; and we explicitly verify that the resulting low-energy effective action is compatible with the usual gauge invariance requirements. With these results, we complete the one-loop renormalization of the model at the leading order in the Lorentz-violating parameters.

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arXiv2022

Gravitational corrections to a non-Abelian gauge theory

This paper is part of a series of papers exploring the renormalization of field theories coupled to gravity using the effective field theory framework. In previous works we studied the universality of the electric charge and the two-loops beta function in the Einstein-QED system. Now, we use this framework to study the non-Abelian gauge theory with fermions coupled to gravity. We show that even though some of the counterterms are dependent on the gravitational coupling, the renormalized coupling constant, and therefore the beta function, do not receive any gravitational correction at one-loop order. Also, we explicitly show that, at this order, the Slavnov-Taylor identities are respected. Finally, we end the paper putting into perspective the results of the present and the past papers.

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arXiv2021

Universality of gauge coupling constant in the Einstein-QED system

In this paper we discuss the universality of the renormalization of the gauge coupling constant in the quantum electrodynamics coupled to the Einstein's gravity in the framework of effective field theory in an arbitrary gauge. We observe that the renormalization of the three-point functions with different particles receive different contributions from the gravitational sector. Despite that, the universality of the gauge coupling constants is guaranteed by the Ward identity that makes the renormalized electric charge receive no contribution from the gravitational sector at one-loop order.

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arXiv2021

Gravitational corrections to two-loop beta function in quantum electrodynamics

In this work, we use the framework of effective field theory to couple Einstein's gravity to quantum electrodynamics (QED) and determine the gravitational corrections to the two-loop beta function of the electric charge in arbitrary electrodynamics (Lorentz-like) and arbitrary (de Donder like) gravitational gauges. Our results indicate that gravitational corrections do not alter the running behavior of the electric charge; on the contrary, we observe that it gives a positive contribution to the beta function, making the electric charge grow even faster.

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arXiv2021

Effective potential and dynamical symmetry breaking up to five loops in a massless abelian Higgs model

In this paper, we investigate the application of the Renormalization Group Equation (RGE) in the determination of the effective potential and the study of Dynamical Symmetry Breaking (DSB) in a massless Abelian Higgs (AH) model with an N-component complex scalar field in (3+1) dimensional spacetime. The classical Lagrangian of this model has scale invariance, which can be broken by radiative corrections to the effective potential. It is possible to calculate the effective potential using the RGE and the renormalization group functions that are obtained directly from loop calculations of the model and, using the leading logs approximation, information about higher loop orders can be included in the effective potential thus obtained. To show this, we use the renormalization group functions reported in the literature, obtained with a four loop calculation, and obtain a five loop approximation to the effective potential, in doing so, we have to properly take into account the fact that the model has multiple scales, and convert the functions that were originally calculated in the minimal subtraction (MS) renormalization scheme to another scheme which is adequate for the RGE method. This result is then used to study the DSB, and we present evidence for a rich structure of classical vacua, depending on the value of gauge coupling constant and number of scalar fields, which are considered as free parameters.

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arXiv2020

Renormalization group improvement of the effective potential in six dimensions

Using the renormalization group improvement technique, we study the effective potential of a model consisting of $N$ scalar fields $ϕ^i$ transforming in the fundamental representation of $O(N)$ group coupled to an additional scalar field $σ$ via cubic interactions, defined in a six-dimensional spacetime. We find that the model presents a metastable vacuum, that can be long-lived, where the particles become massive. The existence of attractive and repulsive interactions plays a crucial role in such phenomena.

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arXiv2019

Dynamical gauge symmetry breaking in lower-dimensional Lorentz-violating supersymmetric theory

In this work we study the dynamical generation of mass in the Lorentz-violating low-dimensional Super-Yang-Mills theory in the aether superspace coupled to a scalar matter. We also suggest that our studies can be applied for condensed matter systems, especially lower-dimensional superconductors and topological insulators. In low dimensional materials, the parameter $Δ$ generated by presence of the aether term can be interpreted as a quantity that renormalizes the propagation velocity of the bosonic mode with respect to the Fermi velocity.

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arXiv2018

Soft supersymmetry breaking in the nonlinear sigma model

In this work we discuss the dynamical generation of mass in a deformed ${\cal N}=1$ supersymmetric nonlinear sigma model in a two-dimensional ($D=1+1$) space-time. We introduce the deformation by imposing a constraint that softly breaks supersymmetry. Through the tadpole method, we compute the effective potential at leading order in $1/N$ expansion showing that the model exhibit a dynamical generation of mass to the matter fields. Supersymmetry is recovered in the limit of the deformation parameter going to zero.

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arXiv2018

$CP^{(N-1)}$ model in aether-superspace

In this paper we study the dynamical generation of mass in the Lorentz-violating $CP^{(N-1)}$ model defined in two and three-dimensional aether-superspace. We show that even though the model presents a phase structure similar to the usual, Lorentz invariant case, the dynamically generated mass by quantum corrections has a dependence on the Lorentz violating background properties, except for spacelike LV vector parameter. This is to be contrasted with the behavior of the quantum electrodynamics in the two-dimensional aether-superspace, where the dynamical generation of mass was shown to exhibit an explicit dependence on the aether parameters in every possible case.

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arXiv2016

Renormalization Group Improvement and Dynamical Breaking of Symmetry in a Supersymmetric Chern-Simons-matter Model

In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2+1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.

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arXiv2016

Effective field theory of quantum gravity coupled to scalar electrodynamics

In this work we use the framework of effective field theory to couple Einstein's gravity to scalar electrodynamics and determine the renormalization of the model through the study of physical processes below Planck scale, a realm where quantum mechanics and general relativity are perfectly compatible. We consider the effective field theory up to dimension six operators, corresponding to processes involving one graviton exchange. Studying the renormalization group functions we see that the beta function of the electric charge is positive and possesses no contribution coming from gravitational interaction. Our result indicates that gravitational corrections do not alter the running behavior of the gauge coupling constants, even if massive particles are present.

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arXiv2015

Lorentz-violating quantum electrodynamics in two-dimensional aether-superspace

The two-dimensional aether-superspace is constructed and the superfield techniques are applied to the study of dynamical generation of mass in the Lorentz-violating supersymmetric quantum electrodynamics in two dimensions of spacetime. It is shown that such model presents a dynamical generation of mass to the gauge aether-superfield and its dispersion relation has the structure similar of the CPT-even Lorentz-breaking models.

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arXiv2015

Kählerian Effective Potentials for Chern-Simons-Matter Theories

In this paper, we will calculate the effective potential for a theory of multiple M2-branes. As the theory of multiple M2-branes can be described by a Chern-Simons-matter theory, this will be done by calculating the Kählerian effective potential for a Chern-Simons-matter theory. This calculation will be performed in $\mathcal{N} = 1$ superspace formalism. We will initially study an Abelian Chern-Simons-matter theory, and then generalize those results to the full non-Abelian Chern-Simons-matter theory. We will obtain explicit expressions for the superpropagators for this theory. These superpropagators will be used to calculate the one-loop effective potential.

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