Searcharxiv⌕ Search

arXiv subjects

A. C. Lehum

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

At least 19 recordsLinked to original sources
arXiv2026

Scalar fields, impurities and supersymmetry

We develop a rigid $\mathcal{N}=(1,1)$ superspace formulation for multifield scalar models coupled to localized impurities through spurion superfields in two-dimensional spacetime. The spurionic completion gives a manifestly supersymmetric action and provides a systematic framework for describing interacting scalar fields in the presence of impurity backgrounds. In this setting, supersymmetry acts as an organizing principle for a controlled bosonic half-BPS sector, with the preserved projector selecting the impurity-compatible first-order equations. We derive the corresponding coupled BPS equations, energy density, boundary conditions, and Bogomol'nyi bound, showing that localized impurities deform the BPS profiles and redistribute the local energy density while leaving the total BPS energy fixed by the topological boundary term. We illustrate the formalism through representative one-, two-, and three-field models, analyzing the resulting BPS configurations and their local energy density profiles.

hep-th↗
arXiv2026

Lorentz violating quadratic gravity

In this paper, we explore the perturbative renormalization and study the classical dynamics of the bumblebee model coupled to quadratic gravity, a theoretical setting that allows the violation of Lorentz symmetry. Such a violation arises from a vector field whose potential is engineered to induce a nonzero vacuum expectation value (VEV), thereby leading to the emergence of a preferred direction in spacetime and, consequently, to the spontaneous breaking of Lorentz symmetry. Working in dimensional regularization and expanding the metric around flat space, we compute the one-loop divergent parts of the two-point functions of the bumblebee and graviton fields, with special emphasis on the role of Lorentz-violating insertions in internal lines. These results determine the counterterms required to renormalize the gravitational and bumblebee sectors in the presence of a preferred background direction, and make explicit how Lorentz-violating interactions feed back into the UV structure of quadratic gravity. On the classical side, we derive the field equations and identify exact solutions supported by bumblebee backgrounds. In particular, we show that the Schwarzschild and de Sitter geometries remain exact solutions for an appropriate bumblebee field profile, even in the presence of one of the non-minimal couplings. We close with a discussion of the operator content suggested by the one-loop structure and of prospective extensions to cosmological and less symmetric backgrounds.

hep-th↗
arXiv2026

Perturbative Analysis of CPT-Odd Lorentz-Violating Scalar QCD

We perform a complete one-loop renormalization analysis of CPT-odd Lorentz-violating scalar quantum chromodynamics with adjoint scalar matter. Working to first order in the preferred background vector and treating the corresponding operators as perturbative insertions, we compute the ultraviolet-divergent parts of the relevant two-, three-, and four-point Green's functions for the gauge, scalar, and ghost fields. We show that the gauge sector develops the expected Carroll-Field-Jackiw-type correction, which generically turns out to be divergent in our theory, although the divergence vanishes in a certain gauge, while the scalar sector displays the corresponding CPT-odd single-derivative term proportional to the background vector. We further demonstrate that several of the Lorentz-violating corrections the three- and four-point function are ultraviolet finite. All one-loop divergences may be absorbed into counterterms already allowed by the classical Lagrangian, providing an explicit proof of the multiplicative renormalizability of the theory at this order. We also obtain the associated renormalization constants and one-loop $β$-functions for the gauge coupling, the Lorentz violation parameters, and the scalar self-interaction.

hep-th↗
arXiv2026

Complex bumblebee model

We formulate a renormalizable complex extension of the bumblebee theory in which the bumblebee field is promoted to a complex one and coupled to an Abelian gauge sector. Besides the minimal gauge covariant interaction, the model includes a longitudinal kinetic term controlled by a dimensionless parameter $g_l$ and a non-minimal magnetic-type coupling $g_m$ between the complex bumblebee and the photon. Using dimensional regularization and minimal subtraction, we determine the one-loop UV divergences of the two-, three-, and four-point functions relevant to the renormalization of the gauge, longitudinal, and quartic sectors. We obtain the corresponding counterterms and derive the one-loop renormalization-group functions for $e$, $g_l$, $g_m$, and the bumblebee self-couplings $λ$ and $\tildeλ$. Motivated by the known gauge- and field-reparametrization subtleties of the conventional Coleman--Weinberg analysis, we formulate an RG-covariant leading-logarithmic improvement scheme for the Vilkovisky--DeWitt effective potential in normal field coordinates, in which the RG operator is governed solely by the beta functions. We apply this framework to a real constant bumblebee background and obtain the leading-logarithmic one-loop effective potential, discussing the conditions under which a nontrivial vacuum is generated by dimensional transmutation and thereby provides a dynamical realization of Lorentz symmetry breaking in this class of models.

hep-th↗
arXiv2026

Half-BPS Impurity Backgrounds and Supersymmetry

We develop a rigid $\mathscr{N} =(1,1)$ superspace framework for spatially inhomogeneous impurity deformations in $D=1+1$ dimensions by embedding the impurity profile into a real background superfield (spurion). This spurionic completion provides a manifestly supersymmetric description at the level of the action and offers a systematic route to identify which inhomogeneous backgrounds preserve a nontrivial subset of supercharges. Focusing on static interface-type configurations, we determine the half-BPS condition on the spurion background and the corresponding supersymmetry projector. In the resulting half-BPS sector we derive the associated first-order BPS equation for static bosonic matter configurations and establish an exact Bogomol'nyi completion of the static energy, yielding a sharp bound saturated by BPS solutions. We further comment on how explicit coordinate dependence and derivative-dependent impurity couplings can obstruct the Bogomol'nyi structure, thereby motivating spurionic extensions that retain supersymmetric control over inhomogeneous deformations.

hep-th↗
arXiv2026

Scattering amplitudes in dimensionless quadratic gravity coupled to QED

We study ultra-Planckian $2\to2$ scattering in an Abelian gauge theory coupled to agravity, the scale-free and renormalizable realization of quadratic quantum gravity. Focusing on charged fermions and scalars interacting with the photon and the higher-derivative graviton, we present compact analytic expressions for the unpolarized squared matrix elements for a broad set of tree-level processes, including photon--photon, fermion--fermion, fermion--photon, scalar--fermion, scalar--photon, scalar--scalar, and annihilation channels. In contrast to purely graviton-mediated analyses, we retain systematically the photon--graviton interference contributions and verify explicitly the independence of the results on the gravitational gauge-fixing parameter. The amplitudes display characteristic forward/backward enhancements associated with small momentum transfer, amplified by the $1/p^{4}$ graviton propagator, while their high-energy scaling reflects the underlying dimensionless gravitational couplings. Moreover, for all channels analyzed the corresponding differential cross sections exhibit the universal ultra-Planckian scaling $dσ/dΩ\propto 1/s$, where $s$ is the Mandelstam invariant (the squared center-of-momentum energy). Our results furnish a unified amplitude-level description of how higher-derivative gravity reshapes familiar QED scattering at ultra-Planckian energies and provide analytic building blocks for further studies of IR definitions and UV consistency in agravity with matter.

hep-th↗
arXiv2025

Modified Euler-Heisenberg effective action and Proper-Time Method in Lorentz-Violating Scalar QED

Quantum photon effects in vacuum provide an interesting setting to test quantum electrodynamics, serving as a source for predictions about physics beyond the Standard Model. In this paper, we investigate these effects by calculating the one-loop Euler-Heisenberg-like effective action within a Lorentz-violating scalar quantum electrodynamics framework. In both CPT-even and CPT-odd scenarios, we obtain the exact result in all orders of the stress tensor $F_{μν}$ and evaluate explicitly the lower orders of this effective action. We identify the quantum effects coming from Lorentz violation in an explicitly gauge invariant way. Nonlinear Lorentz-violating contributions that may affect photon-photon scattering are explicitly evaluated.

hep-th↗
arXiv2025

On the physical running of the electric charge in a dimensionless theory of gravity

We revisit the renormalization of the gauge coupling in massless QED coupled to a scaleless quadratic theory of gravity. We compare two alternative prescriptions for the running of the electric charge: (i) the conventional $μ$-running in minimal subtraction, and (ii) a ''physical'' running extracted from the logarithmic dependence of amplitudes on a hard scale $Q^{2}$ (e.g., $p^{2}$ or a Mandelstam invariant) after removing IR effects. At one loop, using dimensional regularization with an IR mass regulator $m$, we compute the photon vacuum polarization. We find a clean separation between UV and soft logarithms: the former is gauge and process independent and fixes the beta function, whereas the latter encodes nonlocal, IR-dominated contributions that may depend on gauge parameters and must not be interpreted as UV running. In the quadratic-gravity sector, the photon self-energy is UV finite--the $\lnμ^{2}$ pieces cancel--leaving only $\ln(Q^{2}/m^{2})$ soft logs. Consequently, quadratic gravity does not modify the one-loop UV coefficient and thus does not alter $β(e)$. Therefore, the physical running coincides with the $μ$-running in QED at one loop. Our analysis clarifies how to extract a gauge and process independent running in the presence of gravitational interactions and why soft logs from quadratic gravity should not contribute to $β(e)$.

hep-th↗
arXiv2025

Ultra-Planckian quark and gluon scattering in agravity

We investigate tree-level scattering processes involving quarks ($q$) and gluons ($g$) mediated by graviton exchange in the framework of Agravity, a dimensionless and renormalizable theory of quadratic quantum gravity. Focusing on the ultra-Planckian regime, characterized by the Mandelstam variable $s = (p_1 + p_2)^2$, which corresponds to the total energy squared in the center-of-momentum frame, being much larger than any particle mass scale, we compute the squared amplitudes and analyze the differential cross sections for the processes $gg \to gg$, $gg \to q\bar{q}$, $gq \to gq$, and $qq \to qq$. We demonstrate that all amplitudes scale as $1/s$ at high energies, in agreement with expectations for a UV-complete theory of gravity. In addition, we explore the issue of unitarity in the presence of higher-derivative ghost modes by analyzing the positivity properties of the squared amplitudes. While IR divergences appear in the forward scattering of massless particles, we show that these are regularized by finite quark masses. Our findings support the viability of Agravity as a perturbatively unitary and UV-complete extension of general relativity, capable of consistently describing gravitational interactions among elementary matter fields at trans-Planckian energies.

hep-th↗
arXiv2025

Perturbative aspects of the supersymmetric three-dimensional massive QED

We perform the study of perturbative aspects of a three-dimensional supersymmetric Maxwell-Chern-Simons-Proca theory minimally coupled to scalar superfields. Using the superfield formalism, we derive the propagators for both gauge and matter superfields and compute the leading quantum corrections to the effective action. The presence of the Proca-like term explicitly breaks gauge invariance, modifying the structure of the gauge superfield propagator and leading to an essentially new form of quantum contributions in comparison with the usual QED. We analyze the Feynman diagrams that contribute to the quadratic part of the effective action, obtaining corrections to both the kinetic and mass terms of the scalar superfields. Furthermore, we discuss the UV behavior of the model, considering its renormalization properties and the possibility of perturbative finiteness to all loop orders, similar to supersymmetric QED$_3$. Finally, we highlight potential applications of this model in condensed matter systems and possible connections with modified supersymmetric electrodynamics and dualities in lower-dimensional theories.

hep-th↗
arXiv2025

One-loop corrections in Maxwell-metric-affine bumblebee gravity

In this paper, we consider the coupling of the metric-affine bumblebee gravity to the Abelian gauge field and obtain the effective model corresponding to the weak gravity limit of this theory. The effective bumblebee theory displays new unconventional couplings between the bumblebee field and its field strength, and the $U(1)$ gauge field along with its respective field strength, as a result of the non-metricity effects. Thus, being a new gauge-bumblebee theory, it represents an example of vector-vector couplings which are very rarely considered, if not entirely overlooked, in the Abelian case. For this theory we calculate the lower perturbative corrections. We close the paper with discussions of other possible vector-vector couplings.

hep-th↗
arXiv2024

Dynamical Lorentz Symmetry Breaking in a Scale-free Theory of Gravity

This paper explores the renormalization of scale-free quadratic gravity coupled to the bumblebee field and its potential for dynamically breaking Lorentz symmetry. We conduct one-loop renormalization of the model and calculate the associated renormalization group functions. Furthermore, we compute 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. This spontaneous breaking of scale invariance, driven by the non-zero VEV of the bumblebee field, leads to Lorentz symmetry violation. As a result, the non-minimal coupling between the bumblebee and gravitational fields induces a spontaneous generation of an Einstein-Hilbert term via radiative corrections, suggesting a possible link between the Planck scale and Lorentz violation phenomena.

hep-th↗
arXiv2024

Gravitational corrections to the two-loop beta function in a non-Abelian gauge theory

This paper investigates the coupling of massive fermions to gravity within the context of a non-Abelian gauge theory, utilizing the effective field theory framework for quantum gravity. Specifically, we calculate the two-loop beta function of the gauge coupling constant in a non-Abelian gauge theory, employing the one-graviton exchange approximation. Our findings reveal that gravitational corrections may lead to a non-trivial UV fixed point in the beta function of the gauge coupling constant, contingent upon the specific gauge group and the quantity of fermions involved.

hep-th↗
arXiv2024

Two-loop corrections to the Carroll-Field-Jackiw term in a CPT-odd Lorentz-violating scalar QED

In this study, we systematically calculate one-loop corrections to the Lorentz-violating vertices within the framework of CPT-odd Quantum Electrodynamics, encompassing scalar and photon fields in arbitrary gauge. Additionally, we ascertain the finite two-loop corrections to the Carroll-Field-Jackiw term. Furthermore, we analyze the UV divergent component of the two-loop Lorentz-violating correction in the self-energy of the scalar field.

hep-th↗
arXiv2023

Two-loop renormalization of the CPT-even Lorentz-violating Scalar QED

Investigating quantum effects arising from high loops in perturbation theory is crucial for the physical applications of any quantum field theory. This paper presents a comprehensive analysis of the two-loop renormalization of CPT-even Lorentz-violating scalar electrodynamics at the first order in the background vectors. We provide results for the self-energies of the photon and scalar field, as well as for the three-point function associated with the scalar-scalar-photon vertex, ensuring a thorough examination of the quantum effects. The calculations satisfy the ward identities, demonstrating their consistency. Computational tools were employed to carry out the calculations, and we provide additional details in the Supplemental Material for interested readers. Our contribution presents, for the first time, a two-loop calculation within the framework of the Lorentz-violating Standard Model Extension.

hep-th↗
arXiv2023

Perturbative aspects of mass dimension one fermions non-minimally coupled to electromagnetic field

This paper addresses perturbative aspects of the renormalization of a fermion with mass dimension one non-minimally coupled to the electromagnetic field. Specifically, we calculate the one-loop corrections to the propagators and vertex functions of the model and determine the one-loop beta function of the non-minimal electromagnetic coupling. Additionally, we perform calculations of the two-loop corrections to the gauge field propagator, demonstrating that it remains massless and transverse up to this order. We also find that the non-minimal electromagnetic coupling can exhibit asymptotic freedom if a certain condition is satisfied. As a potential dark matter candidate, these findings suggest that the field may decouple at high energies. This aspect holds significance for calculating the relic abundance and freeze-out temperature of the field, particularly in relation to processes involving the ordinary particles of the Standard Model.

hep-ph↗
arXiv2023

Perturbative Aspects of CPT-Even Lorentz-Violating Scalar Chromodynamics

In this work, we formulate the theory of Lorentz-violating scalar Quantum Chromodynamics with an arbitrary non-Abelian gauge group. This theory belongs to the class of models encompassed by the standard model extension framework. At the lowest order in the theory's Lorentz violation parameters, we calculate the divergent quantum corrections, including the renormalization group $β$-functions of the theory. The Lorentz-violating sector is shown to be scale invariant if there is a particular relation between the couplings.

hep-th↗