arXiv subjects

Ilya L. Shapiro

Publications and source records attributed to Ilya L. Shapiro.

At least 19 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

Renormalization group corrections to $Λ$CDM model and observational consequences for $H_0$ tension

We explore the renormalization group-based extension of the $Λ$CDM model as a potential solution to the current cosmological tensions. In this approach, both the cosmological constant density and Newton's constant are allowed to vary with the energy scale, as a consequence of the remnant effects of massive quantum fields in the low-energy regime. The corresponding cosmological model is consistent with the principles of quantum field theory, based on the covariance of the vacuum effective action, and is characterized by an unique extra parameter $ν$. Our analysis yields a best-fit value of $ν= - (2.5 \pm 1.3)\times 10^{-4}$, placing the $Λ$CDM limit at the $2σ$ region of the $ν$ posterior. This narrow range is consistent with data from CMB (Planck), BAO (DESI), and SN Ia (DES Y5). Our result also alleviates the $H_0$ tension and is consistent with the previously established constraints from large-scale structure. In these kind of models, there is a link between cosmology and particle physics. Our results point to possibility of a new physics, characterized by a mass spectrum lying below the Planck scale but above the values typically associated with Grand Unified Theories (GUTs).

astro-ph.CO↗

arXiv2026

Bounce solutions with quantum vacuum effects of massive fields and subsequent Starobinsky inflation

We extend the previous work about the cosmological solutions with a bounce without modifications of gravity or introducing an extra scalar field. The main finding was that the bounce is possible in the initially contracting Universe filled with matter. After a strong contraction, matter gains the equation of state close to the one of radiation, such that the effect on matter on the evolution of the FLRW metric disappears at the classical level. However, this effect comes back owing to the quantum trace anomaly in the matter/radiation sector. In the present contribution, we explore the weak impact of massive fields on the anomaly-driven bounce solution and discuss the role of the vacuum terms. The masses are assumed small and regarded as small perturbations, which enables using trace anomaly even in this case. On the other hand, by adding the $R^2$ term to the action, we arrive at the model with the trans-Planckian bounce and subsequent Starobinsky inflation. In such a framework, using the numerical analysis, we consider three scenarios providing bounce solutions.

gr-qc↗

arXiv2026

Low-energy limit in the anomaly-induced action and the semiclassical cosmological bounce

In the recently proposed scenario, the cosmological bounce occurs because the initially contracting Universe is not empty. In the region close to singularity, matter contents of the Universe heat up and effectively become radiation. Then, the trace anomaly automatically provides bounce if the overall beta function in the matter sector is positive. Independent of the remaining open questions on the quantum field theory side, it is interesting to consider this model from the cosmological perspective. In the present work, we develop the general formalism which is a necessary step for exploring the primordial cosmological perturbations. The main technical development is the formulation of the low-energy version for the nonlocal part of the effective action. The complete form of this action can be done local using two auxiliary scalars. In our new version, there are more scalars, but this enables one to avoid higher derivatives.

gr-qc↗

arXiv2026

On the Renormalization in Conformal Quantum Gravity

One-loop divergences in classically conformal theory in curved spacetime is a nontrivial issue if the theory under consideration possesses gauge invariance. In this case, quantization involves introducing the gauge-fixing term and the action of ghosts, both of which are not conformal. The formal proof of the conformal invariant renormalizability in this situation, including interacting theories, has been given in the paper from 1984 by one of the present authors. Owing to BRST symmetry, the contributions of the gauge-fixing and ghost sectors to the conformal variation of the effective action cancel each other. This cancellation does not hold in the finite part of the one-loop and higher-loops effective action, that results in the anomaly. In this paper, we extend the early results on conformal matter fields in external gravitational field and apply them to conformal quantum gravity, including the case of conformal gravity coupled to other conformal matter fields. The gauge-fixing in the Weyl-squared gravity is more complicated, nevertheless, the proof of the one-loop conformal invariant renormalization using BRST symmetry is possible. As a preliminary to conformal quantum gravity, we also present a detailed general proof of conformal invariant one-loop divergences in the corresponding semiclassical theory.

hep-th↗

arXiv2026

On the total derivative divergence for a nonminimal vector operator

We report on the calculation of the total derivative $\Box R$ term in the divergence of vacuum effective action for the nonminimal vector field operator in a curved space background. This term led to an interesting discussions in the literature, in particular because it defines the local part of anomaly-induced effective action in conformal quantum gravity and may be decisive for the renormalizability of this theory. The divergent term of our interest was previously derived several times. One of the main results is that the mentioned local term is gauge-fixing dependent in the case of electromagnetic field, that contradicts the general theorems about quantum corrections. We perform the derivation by using Riemann's normal coordinates and confirm the previous results. The discussion includes the possible role of the gauge-dependent IR regulators and the related ambiguity.

hep-th↗

arXiv2026

Trace anomaly, effective approach, and gravitational potential

We explore and discuss corrections to the Newton potential from the quantum effects of conformal matter fields. In this special case, one can compare different approaches, including that of effective quantum gravity and another, based on the conformal (trace) anomaly. The comparison of these two methods is the main focus in the present work. Using the anomaly-induced effective action of gravity requires fixing the quantum vacuum state, similar to what is done in the description of black hole evaporation. In the Boulware vacuum state, we compute the anomaly-induced stress tensor and the first-order correction to the classical gravitational law. The quantum correction to the Newton's potential derived in this way, differs from the result calculated in a way analogous to the effective approach to quantum gravity. The only way to reconcile the two approaches for deriving the leading semiclassical corrections to Newtonian potential is to modify the asymptotic behavior of the average of the energy-momentum tensor in the Boulware vacuum state, as has been recently discussed in the literature.

hep-th↗

arXiv2026

Bound states of massive complex ghosts in superrenormalizable quantum gravity theories\

One of the remarkable differences between renormalizable quantum gravity with four-derivative action and its superrenormalizable polynomial generalizations is that the latter admit a more sophisticated particle mass spectrum. Already in the simplest superrenormalizable case, the theory has a six-derivative Lagrangian, admitting either a real or complex spectrum of masses. In the case of a real spectrum, there are the graviton, massive unphysical ghosts, and normal particles with masses exceeding the ones of the ghosts. It is also possible to have pairs of complex conjugate massive ghost-like particles. We show that in both cases, these theories do not admit a Källén-Lehmann representation and do not satisfy the positivity criterium of consistency in terms of the fields associated to those particles. In the main part of the work, using a relatively simple Euclidean scalar toy model, we show that the theory with complex spectrum forms bound states confining unphysical massive excitations into a normal composite particle. Finally, we discuss the cosmological implications of such a ghost confinement.

gr-qc↗

arXiv2025

Trace anomaly for a conformal 2D vector field model

The trace anomaly and anomaly-induced action are evaluated for the two-dimensional $2D$ vector theory with classical conformal symmetry. Implementing local conformal symmetry while preserving the gauge invariance requires either giving up locality of the classical action or, equivalently, introducing an auxiliary scalar field. The two-dimensional limit in such a theory is singular. However, in the dimensional regularization, the limit $D \to 2$ in the one-loop divergence is smooth. As a result, we arrive at the expression for anomaly, which has a rich general structure, typical for the dimensions $D \geq 4$. For comparison and completeness, we also evaluate anomalies for conformal scalar and fermions, also in the presence of auxiliary external scalars.

hep-th↗

arXiv2025

Reflection positivity in a higher-derivative model with physical bound states of ghosts

The inclusion of higher derivatives is a necessary condition for a renormalizable or superrenormalizable local theory of quantum gravity. On the other hand, higher derivatives lead to classical instabilities and a loss of unitarity at the quantum level. A standard way to detect such issues is by examining the reflection positivity condition and the existence of a Kallen-Lehmann spectral representation for the two-point function. We demonstrate that these requirements for a consistent quantum theory are satisfied in a theory we have recently proposed. This theory is based on a six-derivative scalar field action featuring a pair of complex-mass ghost fields that form a bound state. Our results support the interpretation that physical observables can emerge from ghost dynamics in a consistent and unitary framework.

hep-th↗

arXiv2025

Six-dimensional cosmological models with conformal extensions

We consider the background cosmological solutions in the $6D$ (six-dimensional) model with one time and five space coordinates. The theory of our interest has the action composed by the Einstein term, cosmological constant, and two conformal terms constructed from the third powers of the Weyl tensor. It is shown how the highest derivative terms in the equations of motion can be isolated that opens the way for their numerical integration. There are flat anisotropic solutions which make one of the flat isotropic subspaces to be static. Depending on the value of bare cosmological constant, either two-dimensional or three-dimensional subspace can be static. In particular, there is a physically favorable solution with three ``large'' space coordinates and two extra inner dimensions stabilized. This solution is stable for a wide range of coupling constants, but this requires a special value of the bare cosmological constant.

gr-qc↗

arXiv2025

Renormalizable quantum field theory in curved spacetime with external two-form field

We argue that the renormalizability of interacting quantum field theory on the curved-space background with an additional external antisymmetric tensor (two-form) field requires nonminimal interaction of the antisymmetric field with quantum fermions and scalars. The situation is qualitatively similar to the metric and torsion background. In both cases, one can explore the renormalization group running for the parameters of nonminimal interaction and see how this interaction behaves in the UV limit. General considerations are confirmed by the one-loop calculations in the well-known gauge model based on the $SU(2)$ gauge group.

hep-th↗

arXiv2025

On the new way of symmetry breaking in scalar QED and the one-loop renormalization

It is well known that single real scalar field does not allow gauge coupling to the Abelian vector field. Using the complex scalar model as a starting point, we construct the Abelian gauge model with two real scalars. The gauge transformations for the scalars look different (albeit equivalent) from the conventional sQED. Spitting the masses of the scalars, or the scalar self-couplings, or the nonminimal parameters of scalar-curvature interaction, we arrive at a qualitatively new way of gauge symmetry breaking. Using the Schwinger-DeWitt technique, we explore the one-loop renormalization of this new model in curved spacetime.

physics.gen-ph↗

arXiv2025

Derivative expansion in a two-scalar field theory

The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term is calculated up to the first order in curvature in the one-scalar theory. The two-scalar problem is solved by extracting normal modes and consequent reduction to the single-scalar case. The method can be applied to a larger number of scalars. In the theory with strong hierarchy of masses, the renormalized effective potential and the coefficients of the second-order derivative terms demonstrate the quantum decoupling in the low-energy limit.

hep-th↗

arXiv2025

Local conformal symmetry and anomalies with antisymmetric tensor field

We consider the trace anomaly, which results from the integration of the massless conformal fermion field with the background of metric and antisymmetric tensor fields. The non-local terms in the anomaly-induced effective action do not depend on the scheme of quantum calculations. On the other hand, total derivative terms in the anomaly and the corresponding local part of the induced action manifest scheme dependence and multiplicative anomaly.

hep-th↗

arXiv2025

Decoupling theorem and effective quantum gravity

This is a contribution to the memorial edition devoted to Professor Vladislav Gavrilovich Bagrov, who was my official adviser from the beginning of undergraduate period to the end of Ph.D. The text includes a mentioning of two my publications in Izvestia VUZov Fisica (Russian Physics Journal), where Vladislav Gavrilovich served as an Editor. The rest of this paper is based on the recent lectures about decoupling in quantum gravity, given in ICTP-SAIFR in Sao Paulo and at the school ``Estate Quantistica'' in Scalea, Italy. After a brief and mainly qualitative review of the decoupling theorem in semiclassical gravity and the scalar fourth-derivative model of Antoniadis and Mottola, we explain what is the expected result for the physical beta functions in fourth-derivative quantum gravity and what should remain from these beta functions in the IR.

hep-th↗

arXiv2025

Antisymmetric Tensor Field and Cheshire Cat Smile of the Local Conformal Symmetry

The conformal version of the antisymmetric second-order tensor field in four spacetime dimensions does not have gauge invariance extensively discussed in the literature for more than half a century. Our first observation is that, when coupled to fermions, only the conformal version provides renormalizability of the theory at the one-loop level. General considerations are supported by the derivation of one-loop divergences in the fermionic sector, indicating good chances for asymptotic freedom. The arguments concerning one-loop renormalizability remain valid in the presence of self-interactions and the masses for both fermion and antisymmetric tensor fields. In the flat spacetime limit, regardless of the conformal symmetry has gone, there is an expectation to meet renormalizability in all loop orders.

hep-th↗

arXiv2024

Pauli equation and charged spin-1/2 particle in a weak gravitational field

Using the nonrelativistic approximation in the curved-space Dirac equation, the analog of the Pauli equation is derived for a weak gravitational field with a gauge fixing condition related to the synchronous gauge, in the presence of an electromagnetic field. Different from the previous works which were employing either the exact or conventional Foldy-Wouthuysen transformations, here we perform calculations by directly performing nonrelativistic approximation which reduced in the power series expansion in the inverse mass of the spinning particle. On top of that, the equations of motion for the massive spin-$1/2$ charged particle are obtained. The two particular cases of the previously explored backgrounds, namely a) plane gravitational wave and b) homogeneous static gravitational field are considered for control. In the case a) we meet correspondence with the previous results. On the other hand, in case b), there is no correspondence with neither perturbative nor with exact Foldy-Wouthuysen transformations, which we also recalculate and agree with the previous works. The disagreement is a kind of a theoretical challenge and most likely occurs because the potential energy, in the particular case of Newtonian approximation, is proportional to the mass of the particle.

gr-qc↗