arXiv subjects

Lesław Rachwał

Publications and source records attributed to Lesław Rachwał.

14 recordsLinked to original sources

arXiv2025

Visions in Quantum Gravity

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

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arXiv2024

Running of the Number of Degrees of Freedom in Quantum Conformal Gravity

We study how the number of degrees of freedom in Weyl conformal gravity runs with the energy scale from the UV fixed point. To this end we employ two approaches. First, we utilize the Fradkin--Tseytlin prescription for the number of degrees of freedom and demonstrate that the one-loop results are highly dependent on the selected background. We then employ the counting methodology based on the $a$- and $c$-functions, which are typically used to characterize the trace anomaly of conformal field theory in four dimensions. We compute these in the enhanced one-loop approximation and demonstrate that the degrees of freedom decrease monotonically from six degrees in the UV regime. This behavior is independent of the backgrounds considered. Finally, we show how to relate the Fradkin--Tseytlin prescription to counting based on the $a$- and $c$-functions.

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arXiv2024

Generalization of conformal Hamada operators

The six-derivative conformal scalar operator was originally found by Hamada in its critical dimension of spacetime, $d=6$. We generalize this construction to arbitrary dimensions $d$ by adding new terms cubic in gravitational curvatures and by changing its coefficients of expansion in various curvature terms. The consequences of global scale-invariance and of infinitesimal local conformal transformations are derived for the form of this generalized operator. The system of linear equations for coefficients is solved giving explicitly the conformal Hamada operator in any $d$. Some singularities in construction for dimensions $d=2$ and $d=4$ are noticed. We also prove a general theorem that a scalar conformal operator with $n$ derivatives in $d=n-2$ dimensions is impossible to construct. Finally, we compare our explicit construction with the one that uses conformal covariant derivatives and conformal curvature tensors. We present new results for operators built with different orders of conformal covariant derivatives.

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arXiv2023

Ultraviolet-complete quantum field theories with fractional operators

We explore quantum field theories with fractional d'Alembertian $\Box^γ$. Both a scalar field theory with a derivative-dependent potential and gauge theory are super-renormalizable for a fractional power $1<γ\leq 2$, one-loop super-renormalizable for $γ>2$ and finite if one introduces killer operators. Unitarity is achieved by splitting the kinetic term into the product of massive fractional operators, eventually sending the masses to zero if so desired. Fractional quantum gravity is also discussed and found to be super-renormalizable for $2<γ\leq 4$ and one-loop super-renormalizable for $γ>4$. To make it unitary, we combine the splitting procedure with a fractional generalization of the Anselmi-Piva procedure for fakeons. Among new technical results with wider applications, we highlight the Leibniz rule for arbitrary powers of the d'Alembertian and the Källén-Lehmann representation for a propagator with an arbitrary number of branch cuts.

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arXiv2023

Renormalizability of nonlocal quantum gravity coupled to matter

We extensively study the ultraviolet quantum properties of a nonlocal action for gravity nonminimally coupled to matter. The theory unifies matter and gravity in an action principle such that all the classical solutions of Einstein's theory coupled to matter are also solutions of the nonlocal theory. At the quantum level, we show that the theory is power-counting super-renormalizable in even dimensions and finite in odd dimensions. A simple extension of the model compatible with the above properties is finite also in even dimensions.

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arXiv2022

Classical and quantum nonlocal gravity

This chapter of the Handbook of Quantum Gravity aims to illustrate how nonlocality can be implemented in field theories, as well as the manner it solves fundamental difficulties of gravitational theories. We review Stelle's quadratic gravity, which achieves multiplicative renormalizability successfully to remove quantum divergences by modifying the Einstein's action but at the price of breaking the unitarity of the theory and introducing Ostrogradski's ghosts. Utilizing nonlocal operators, one is able not only to make the theory renormalizable, but also to get rid of these ghost modes that arise from higher derivatives. We start this analysis by reviewing the classical scalar field theory and highlighting how to deal with this new kind of nonlocal operators. Subsequently, we generalize these results to classical nonlocal gravity and, via the equations of motion, we derive significant results about the stable vacuum solutions of the theory. Furthermore, we discuss the way nonlocality could potentially solve the singularity problem of Einstein's gravity. In the final part, we examine how nonlocality induced by exponential and asymptotically polynomial form factors preserves unitarity and improves the renormalizability of the theory.

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arXiv2022

How to understand the Structure of Beta Functions in Six-derivative Quantum Gravity?

We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical structure of the exact on the full quantum level beta functions obtained previously for three couplings in front of generally covariant terms with four derivatives (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet scalar) in minimal six-derivative quantum gravity in $d=4$ spacetime dimensions. The fundamental role here is played by the ratio $x$ of the coupling in front of the term with Weyl tensors to the coupling in front of the term with Ricci scalars in the original action. We draw a relation between the polynomial dependence on $x$ and the absence/presence of enhanced conformal symmetry and renormalizability in the models where formally $x\to+\infty$ in the case of four- and six-derivative theories respectively.

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arXiv2022

Introduction to Quantization of Conformal Gravity

A method for consistent quantization of conformal gravity treating conformal symmetry in a very controllable way is presented. First, we discuss local conformal symmetry in the framework of gravitational interactions, where we view it as an example of a general gauge theory. We also present some early attempts at quantization of conformal gravity and use the generalized framework of covariant quantization due to Faddeev and Popov. Some salient issues such as the need for conformal gauge-fixing, an issue with conformal third ghosts, and discontinuities in conformal gravity are studied as well. Finally, we provide some explanations of the original ad hoc methods of computation valid at the first quantum loop level in conformal gravity.

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arXiv2021

On the vector conformal models in an arbitrary dimension

The conventional model of the gauge vector field is invariant under the local conformal symmetry only in the four-dimensional space ($4d$). Conformal generalization to an arbitrary dimension $d$ is impossible even for the free theory, differently from scalar and fermion fields. We discuss how to overcome this restriction and eventually construct four vector conformal actions. One of these models is the particular case of the previously known conformal theory of $n$-forms and others are new, up to our knowledge. In some of these models the gauge invariance is preserved, two of the new models are described by local actions with auxiliary compensating scalar fields, and the extended version of one of these models is on shell equivalent to the last, non-analytic, purely metric version.

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arXiv2021

Infrared behavior of Weyl Gravity

In this paper, we introduce and motivate the studies of Quantum Weyl Gravity (also known as Conformal Gravity). We discuss some appealing features of this theory both on classical and quantum level. The construction of the quantum theory is described in detail to the one-loop level. To facilitate computations we use only physical degrees of freedom, which are singled out through the York decomposition. At the one-loop level we compute the partition function around a general Einstein space. Next, the functional renormalization group of couplings in Quantum Weyl Gravity is investigated. We reproduce completely previous results obtained on maximally symmetric and Ricci-flat backgrounds. Finally, we comment on further directions and on the issue of conformal anomaly.

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arXiv2020

On the regularization of Lifshitz-type field theories

We consider Lifshitz-type scalar theories with explicit breaking of the Lorentz symmetry that, in addition, exhibit anisotropic scaling laws near the ultraviolet fixed point. Using the proper time regularization method on the spatial coordinates only, we derive the regularized form of the one-loop effective potential in such theories. We study the main features of the one-loop effective potential and, also, the RG flow of the scale-dependent potential both in the IR and UV regimes. The beta functions for the couplings are derived.

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arXiv2020

Dark side of Weyl gravity

With the help of a functional renormalization group, we study the dynamical breakdown of scale invariance in quantum Weyl gravity by starting from the UV fixed point that we assume to be Gaussian. To this end, we resort to two classes of Bach-flat backgrounds, namely maximally symmetric spacetimes and Ricci-flat backgrounds in the improved one-loop scheme. We show that apart from a genuine IR fixed point that is reached at a zero value of the running scale, the renormalization group flow also exhibits bouncing behavior. We demonstrate that the IR fixed point found is IR-stable in the space of the considered couplings. As a next step, we analyze physics in the broken phase. In particular, we show that in the low-energy sector of the broken phase, the theory looks like Starobinsky $f(R)$ gravity with a gravi-cosmological constant that has a negative sign in comparison to the usual matter-induced cosmological constant. We discuss implications for cosmic inflation and highlight a non-trivial relation between Starobinsky's parameter and the gravi-cosmological constant. Salient issues, including the scheme independence of the IR fixed point and the role of trace anomaly, are also discussed.

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arXiv2020

Spectral action approach to higher derivative gravity

We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the equivalent forms of the action, which might prove useful in different applications, namely Riemann- and Weyl-dominated representations. The spectral action provides a rather rigid structure of the higher derivative part of the theory. We discuss the possible consequences of this rigidness. As one of the applications, we check whether the conformal backgrounds are preferred in some way on the classical level, with the conclusion that at this level, there is no obvious reason for such a preference, the space $S^1 \times S^3$ studied in earlier works being a special case. Some other possible properties of the higher derivative gravity given by the spectral action are briefly discussed.

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arXiv2018

Unitarity issues in higher derivative field theories

We analyze the unitarity properties of higher derivative quantum field theories which are free of ghosts and ultraviolet singularities. We point out that in spite of the absence of ghosts most of these theories are not unitary. This result confirms the difficulties of finding a consistent quantum field theory of quantum gravity.

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