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A. Yu. Petrov

Publications and source records attributed to A. Yu. Petrov.

At least 19 recordsLinked to original sources
arXiv2026

One-loop contributions in Lorentz-violating scalar QED with nonminimal coupling

In the context of pertubative aspects of Lorentz-violating theories, we study the divergent one-loop two-point functions of a Lorentz-violating (LV) extension of scalar QED containing a dimension-five CPT-odd nonminimal coupling. The model is defined through a generalized covariant derivative involving a constant background vector and the dual electromagnetic field strength. After expanding the action, we derive the full set of vertices relevant for the photon and scalar self-energies, including the mixed minimal-nonminimal seagull interaction diagram required by the gauge invariance. Using dimensional regularization, we compute the divergent parts of the vacuum polarization and scalar self-energy. The complete photon two-point function is shown to be transverse since the mass-dependent pieces generated by the mixed and purely nonminimal bubble graphs cancel against the corresponding seagull graphs, leaving higher-derivative CPT-odd and CPT-even LV gauge counterterms. The scalar self-energy generates LV kinetic and higher-derivative counterterms. The calculation confirms that gauge invariance is preserved, while the nonminimal interaction should be understood within an effective-field-theory expansion.

hep-th↗
arXiv2026

Nonlocal four-fermion theory

In this work, we formulate and analyze a nonlocal four-fermion theory in which the usual Dirac operator is deformed by an entire nonlocal form factor. After introducing an auxiliary scalar field, we derive the mean-field effective action and the corresponding gap equation for the dynamical mass. A central technical point of the analysis is that the nonlocal form factor is a matrix function of the Dirac operator, so the inverse propagator must be treated as an element of the closed algebra generated by the identity and $\not{\!p}$ operators, rather than as a purely scalar quantity. We obtain explicit expressions for the gap kernel for two representative choices of a form factor, $f_{I}(\not{\!\partial})=e^{-\not{\partial}/Λ}$ and $f_{II}(\not{\!\partial})=e^{-i\not{\partial}/Λ}$. Following the IR/UV matching method used in the recent Dirac-like nonlocal spinor theory [1], the momentum integral is split at an intermediate scale $M\ll Ω\ll Λ$, expanded analytically in the infrared and ultraviolet regions, and compared with the usual local NJL/Gross-Neveu result. We show that the hyperbolic form factor enhances the gap integral and lowers the critical coupling, whereas the oscillatory form factor suppresses it and raises the critical coupling. The finite-temperature and finite-density extension is formulated through Matsubara sums and a corrected contour representation, with the local thermal gap equation recovered in the limit $Λ\to\infty$.

hep-th↗
arXiv2026

Induced CFJ Term in nonlocal Lorentz-Violating QED: Natural Regularization from Entire Dirac Operators

We investigate the radiative generation of the Carroll--Field--Jackiw (CFJ) term in nonlocal Lorentz- and CPT-violating extensions of quantum electrodynamics. Nonlocality is introduced through entire nonlocal form factors being functions of the Dirac operator in the fermionic sector. Using the derivative expansion of the one-loop fermionic determinant, we derive the induced CFJ contribution and analyze its ultraviolet (UV) behavior after Wick rotation. For one class of nonlocal form factors, loop integrals become naturally convergent, yielding a finite CFJ coefficient without the need for an external UV regulator. For a second class, the coefficient is rendered finite through an Abel regularization prescription. In both cases, the CFJ structure is preserved while its coefficient is continuously deformed by the ratio between the fermion mass and the nonlocality scale. Our results demonstrate that nonlocality provides a natural framework for controlling UV contributions to radiatively induced topological terms.

hep-th↗
arXiv2026

Nonrotating and rotating black holes with secondary disformal hair in a ghost-free metric-affine parity-violating scalar-torsion theory

In this paper, we formulate a ghost-free metric-affine scalar-torsion model in which a pseudoscalar field is coupled to the Nieh--Yan density and derivatively coupled to the Einstein-Palatini tensor. The theory is projectively invariant and, in the shift-symmetric sector, depends on the scalar only through its gradient. After fixing the projective gauge, the independent connection is solved exactly: its symmetric part is the Levi-Civita connection associated with the metric \(h_{μν}\), disformally related to the metric $g_{μν}$, while its antisymmetric part is a purely axial torsion sourced by $v_μ=\partial_μ\vartheta$. We identify a degenerate ghost-free branch, $α=6β^2κ^2$, for which Ricci-flat geometries in the $h$-metric frame solve the metric equations and the Noether current vanishes identically. For example, we consider Schwarzschild and Kerr geometries in the $h$-metric frame, which generate disformal deformations on these geometries from the perspective of the $g$-metric frame. For the Schwarzschild black hole in the $h$-metric frame, we construct static and Babichev--Charmousis-like time-dependent scalar profiles, and discuss horizon regularity in Eddington--Finkelstein coordinates. For the Kerr black hole in the $h$-metric frame, we show that the fixed-norm scalar profile is generically axisymmetric, depending on both the radial and angular coordinates, and we construct a stationary future-regular profile in ingoing Kerr coordinates. The Kerr solution with the nontrivial scalar field is stealth only in the $h$-metric frame. In the $g$-metric frame, it produces disformal corrections stemming from the nontrivial scalar field profile and it represents secondary disformal scalar hair rather than primary Noether-charge hair.

gr-qc↗
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

Nonrelativistic effective potential of the bumblebee model

In this paper, we explicitly obtain the nonrelativistic Breit potential in the bumblebee model arising in the weak gravity limit of the metric-affine bumblebee gravity, coupled to the spinor matter. In this theory, in the lower (second) order in the small coupling constant $ξ$ (and the second order in the LV vector $β_μ$) it demonstrates the $1/r$ asymptotics, which naturally corresponds to the massless character of the theory, while higher orders in $ξ$ yield anisotropic modifications of the Coulomb potential due to the Lorentz symmetry breaking. For the lower-order modification of the effective potential, we calculate LV corrections to energy levels of the hydrogen atom.

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

Classical investigations in a CPT-even Lorentz-violating model and their implications for the Compton effect

In this work, we investigate some aspects of the Maxwell electrodynamics with the additive Lorentz-violating (LV) CPT-even term. For this model, we derive the energy and momentum conservation laws, highlighting the modifications introduced by Lorentz violation. Furthermore, using the modified dispersion relations, we analyze the correction to Compton effect arising from the presence of the LV vector.

hep-th↗
arXiv2026

Nonlocal spinor superfield theory

In this work, we propose a new three-dimensional nonlocal spinor superfield model. This theory is constructed by introducing form factors in the local spinor superfield action. Then, we couple it minimally to a scalar superfield, for which we calculate the one-loop effective potential as a first constructive example of perturbative calculations in this new theory.

hep-th↗
arXiv2026

A novel nonlocal spin-1/2 theory: classical and quantum aspects

We propose a novel nonlocal spin-1/2 theory in which the form factor depends on the Dirac operator rather than on the d'Alembert operator. In this scenario, we explore some classical and quantum aspects of this new theory. At the classical level, we investigate the dispersion relation of free spin-1/2 particles and find that it increasingly deviates from the standard case as the nonlocal effects become relevant. At the quantum level, we compute the fermionic one-loop effective action for the nonlocal spin-1/2 theory with Yukawa coupling and show that the contributions of nonlocal effects are significant in the UV limit, while in the IR they are suppressed by a UV cutoff scale, which has been chosen to coincide with the nonlocality scale $Λ$. We minimally couple a $U(1)$ gauge field to the nonlocal spin-1/2 field theory and explicitly demonstrate that this theory is gauge invariant. Finally, we obtain a nonlocal version of the Pauli equation and the impact of the nonlocality in the $g$-factor of massive particles.

hep-th↗
arXiv2026

One-loop Euler-Heisenberg action in Lorentz-violating QED revisited

We discuss applications of the proper-time method in a Lorentz-violating extension of QED characterized by the addition of the term proportional to the antisymmetric tensor $H_{μν}$. Unlike other LV extensions of QED, in our case, the one-loop Euler-Heisenberg-like action turns out to include only odd powers of the stress tensor $F_{μν}$. Our result is shown to be UV finite, and it is confirmed using the Feynman diagrams framework.

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

Gravitational lensing by a Lorentz-violating black hole

In this work, we study the gravitational lensing by a Lorentz-violating (LV) black hole inspired by the recent contribution [1]. Explicitly, we concentrate on a specific application: we perform the computation of gravitational lensing effects under the strong field limit. In particular, we analytically derive the deflection angle so that the lens equation can also be addressed. This methodological approach yields physically measurable outcomes, including the determination of relativistic image positions and their corresponding magnifications. As an application of this methodology, we consider the gravitational lensing by Sagittarius A${}^*$ and obtain the corresponding observables expressed as functions of the LV parameter.

gr-qc↗
arXiv2025

Mixed gauge-gravity term and proper time

We consider the four-dimensional action of spinors minimally coupled to a $U(1)$-gauge field in an Riemann-Cartan background. In this theory, we integrate over the spinors and study the resulting one-loop gauge-gravity effective action, paying special attention to the contributions that depend on both the gauge field and the torsion. We explicitly calculate the gauge-torsion term, which turns out to be finite, and comment on possible terms depending simultaneously on torsion, curvature, and gauge field.

hep-th↗
arXiv2025

Metric-affine bumblebee gravity: classical aspects

We consider the metric-affine formulation of bumblebee gravity, derive the field equations, and show that the connection can be written as Levi-Civita of a disformally related metric in which the bumblebee field determines the disformal part. As a consequence, the bumblebee field gets coupled to all the other matter fields present in the theory, potentially leading to nontrivial phenomenological effects. To explore this issue we compute the weak-field, post-Minkowskian limit and study the resulting effective theory. In this scenario, we couple scalar and spinorial matter to the effective metric, and then we explore the physical properties of the VEV of the bumblebee field, focusing mainly on the dispersion relations and the stability of the resulting effective theory.

hep-th↗
arXiv2025

Vacuum Cherenkov radiation for nonminimal dimension-5 Lorentz violation

Vacuum Cherenkov radiation is investigated in the Lorentz-violating Standard-Model Extension for isotropic dim-5 operators $\hat{m}$ and $\hat{a}^μ$ in the fermion sector. Both the kinematics and dynamics of this process are analyzed by analytical and numerical means, leading to its decay and radiated-energy rates as functions of the initial-fermion momentum. We adopt the point of view that vacuum Cherenkov radiation is actually a physical phenomenon expected to occur for a charged, massive fermion in the presence of Lorentz violation, when some additional requirements are satisfied. The absence of this effect in ultrahigh-energy cosmic rays detected on Earth allows us to infer stringent bounds on isotropic dim-5 Lorentz violation in protons, quarks, and electrons.

hep-ph↗