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Sergio L. Cacciatori

Publications and source records attributed to Sergio L. Cacciatori.

At least 19 recordsLinked to original sources
arXiv2025

A gauge theory of complex adaptive systems

We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable case. Bundles' non-triviality naturally arises from local collective interactions between agents. Key elements of the theory of principal and associated bundles, such as local obstructions for triviality and characteristic classes, are opportunely defined in this context. Complexity is modelled as the result of local and topological obstructions for the triviality of these geometric structures.

math-ph↗
arXiv2024

Loops in Anti de Sitter space

We discuss general one and two-loop banana diagrams and one-loop diagrams with external lines with arbitrary masses on the anti de Sitter spacetime by using methods of AdS quantum field theory in the dimensional regularization approach. The banana diagrams explicitly computed in this paper are indeed the necessary ingredients for the evaluation of the two-loop effective potential of the Standard Model and can be used to extend the flat space results in in presence of a negative cosmological constant. In the one-loop case we also compute the effective potential for an $O(N)$ model in $d=4$ dimension as an explicit function of the cosmological constant $Λ$, both exactly and perturbatively up to order $Λ$. In the two-loop case we show the explicit calculation is possible thanks to a remarkable discrete Källén-Lehmann formula which we found and proved sometimes ago and whose domain of applicability we extend in the present paper.

hep-th↗
arXiv2024

Loops in de Sitter space

We discuss general one and two-loops banana diagrams with arbitrary masses on the de Sitter spacetime by using direct methods of dS quantum field theory in the dimensional regularization approach. In the one-loop case we also compute the effective potential for an $O(N)$ model in $d=4$ dimension as an explicit function of the cosmological constant $Λ$, both exactly and perturbatively up to order $Λ$. For the two-loop case we show that the calculation is made easy thanks to a remarkable Kallen-Lehmann formula that has been in the literature for a while. We discuss the divergent cases at d=3 using a contiguity formula for generalized hypergeometric functions and we extract the dominant term at d=4 proving a general formula to deal with a divergent hypergeometric series.

hep-th↗
arXiv2024

Pearcey integrals, Stokes lines and exact baryonic layers in the low energy limit of QCD

The first analytic solutions representing baryonic layers living at finite baryon density within a constant magnetic field in the gauged Skyrme model are constructed. A remarkable feature of these configurations is that, if the Skyrme term is neglected, then these baryonic layers in the constant magnetic background cannot be found analytically and their energies grow very fast with the magnetic field. On the other hand, if the Skyrme term is taken into account, the field equations can be solved analytically and the corresponding solutions have a smooth limit for large magnetic fields. Thus, the Skyrme term discloses the universal character of these configurations living at finite Baryon density in a constant magnetic field. The classical gran-canonical partition function of these configurations can be expressed explicitly in terms of the Pearcey integral. This fact allows us to determine analytically the Stokes lines of the partition function and the corresponding dependence on the baryonic chemical potential as well as on the external magnetic field. In this way, we can determine various critical curves in the ($μ_B-B_{ext}$) plane which separates different physical behaviors. These families of inhomogeneous baryonic condensates can be also dressed with chiral conformal excitations of the solutions representing modulations of the layers themselves. Some physical consequences are analyzed.

hep-th↗
arXiv2022

Intersection Numbers in Quantum Mechanics and Field Theory

By elaborating on the recent progress made in the area of Feynman integrals, we apply the intersection theory for twisted de Rham cohomologies to simple integrals involving orthogonal polynomials, matrix elements of operators in Quantum Mechanics and Green's functions in Field Theory, showing that the algebraic identities they obey are related to the decomposition of twisted cocycles within cohomology groups, and which, therefore, can be derived by means of intersection numbers. Our investigation suggests an algebraic approach generically applicable to the study of higher-order moments of probability distributions, where the dimension of the cohomology groups corresponds to the number of independent moments; the intersection numbers for twisted cocycles can be used to derive linear and quadratic relations among them. Our study offers additional evidence of the intertwinement between physics, geometry, and statistics.

hep-th↗
arXiv2022

The Universal de Rham/Spencer Double Complex on a Supermanifold

The universal Spencer and de Rham complexes of sheaves over a smooth or analytical manifold are well known to play a basic role in the theory of $\mathcal{D}$-modules. In this article we consider a double complex of sheaves generalizing both complexes for an arbitrary supermanifold, and we use it to unify the notions of differential and integral forms on real, complex and algebraic supermanifolds. The associated spectral sequences give the de Rham complex of differential forms and the complex of integral forms at page one. For real and complex supermanifolds both spectral sequences converge at page two to the locally constant sheaf. We use this fact to show that the cohomology of differential forms is isomorphic to the cohomology of integral forms, and they both compute the de Rham cohomology of the reduced manifold. Furthermore, we show that, in contrast with the case of ordinary complex manifolds, the Hodge-to-de Rham (or Frölicher) spectral sequence of supermanifolds with Kähler reduced manifold does not converge in general at page one.

math.AG↗
arXiv2022

Black hole attractors and U(1) Fayet-Iliopoulos gaugings: analysis and classification

We classify the critical points of the effective black hole potential which governs the attractor mechanism taking place at the horizon of static dyonic extremal black holes in $\mathcal{N}=2$, $D=4$ Maxwell-Einstein supergravity with $U(1)$ Fayet-Iliopoulos gaugings. We use a manifestly symplectic covariant formalism, and we consider both spherical and hyperbolic horizons, recognizing the relevant sub-classes to which some representative examples belong. We also exploit projective special Kähler geometry of vector multiplets scalar manifolds, the $U$-duality-invariant quartic structure (and 2-polarizations thereof) in order to retrieve and generalize various expressions of the entropy of asymptotically AdS$_{4}$ BPS black holes, in the cases in which the scalar manifolds are symmetric spaces. Finally, we present a novel static extremal black hole solution to the $STU$ model, in which the dilaton interpolates between an hyperbolic near-horizon geometry and AdS$_{4}$ at infinity.

hep-th↗
arXiv2022

Re-weighting dark matter in disc galaxies: a new general relativistic observational test

A recent analysis of data from the ESA Gaia mission demonstrated that the kinematics of stars in the Milky Way can be modelled without invoking the presence of dark matter whatsoever. Indeed, the higher-than-Keplerian velocities observed in outer stars can be ascribed to the properties of the general relativistic (GR) metric assumed to describe the Galaxy. Here we generalize the concept, and derive the most general exact GR model for a stationary axi-symmetric dynamically cold dust structure. We explicitly show how deviations from the commonly adopted Newtonian dynamics are indeed manifest even at low velocities and low densities. We provide for the first time a detailed description of the frequency shift experienced by photons travelling from any emission site within an external disc galaxy to the observer, relating the outcome of the shift measurement to the gravitational properties of the galaxy. Finally, we devise a novel, groundbreaking observational test potentially able to fully characterize the GR metric under the minimal set of assumptions mentioned above. The proposed experiment exploits the effects non-diagonal GR terms have on the frequency shift of photons, ultimately providing a test to evaluate whether dark matter is actually required by disc galaxy kinematics.

astro-ph.GA↗
arXiv2021

Analytic multi-Baryonic solutions in the SU(N)-Skyrme model at finite density

We construct explicit analytic solutions of the $SU(N)$-Skyrme model (for generic $N$) suitable to describe different phases of nuclear pasta at finite volume in $(3+1)$ dimensions. The first type are crystals of Baryonic tubes (nuclear spaghetti) while the second type are smooth Baryonic layers (nuclear lasagna). Both, the ansatz for the spaghetti and the ansatz for the lasagna phases, reduce the complete set of Skyrme field equations to just one integrable equation for the profile within sectors of arbitrary high topological charge. We compute explicitly the total energy of both configurations in terms of the flavor number, the density and the Baryonic charge. Remarkably, our analytic results allow to compare explicitly the physical properties of nuclear spaghetti and lasagna phases. Our construction shows explicitly that, at lower densities, configurations with $N=2$ light flavors are favored while, at higher densities, configurations with $N=3$ are favored. Our construction also proves that in the high density regime (but still well within the range of validity of the Skyrme model) the lasagna configurations are favored while at low density the spaghetti configurations are favored. Moreover, the integrability property of the present configurations is not spoiled by the inclusion of the subleading corrections to the Skyrme model arising in the 't Hooft expansion. Finally, we briefly discuss the large $N$ limit of our configurations.

hep-th↗
arXiv2021

Towards a full general relativistic approach to galaxies

We analyze the dynamics of a single spiral galaxy from a general relativistic viewpoint. We employ the known family of stationary axially-symmetric solutions to Einstein gravity coupled with dust in order to model the halo external to the bulge. In particular, we generalize the known results of Balasin and Grumiller, relaxing the condition of co-rotation, thus including non co-rotating dust. This further highlights the discrepancy between Newtonian theory of gravity and general relativity at low velocities and energy densities. We investigate the role of dragging in simulating dark matter effects. In particular, we show that non co-rotance further reduce the amount of energy density required to explain the rotation curves for spiral galaxies.

gr-qc↗
arXiv2020

Analytic SU(N) Skyrmions at finite Baryon density

We construct analytic (3+1)-dimensional Skyrmions living at finite Baryon density in the SU(N) Skyrme model that are not trivial embeddings of SU(2) into SU(N). We used Euler angles decomposition for arbitrary N and the generalized hedgehog Ansatz at finite Baryon density. The Skyrmions of high topological charge that we find represent smooth Baryonic layers whose properties can be computed explicitly. In particular, we determine the energy to Baryon charge ratio for any N showing the smoothness of the large N limit. The closeness to the BPS bound of these configurations can also be analyzed. The energy density profiles of these finite density Skyrmions have \textit{lasagna-like} shape in agreement with recent experimental findings. The shear modulus can be precisely estimated as well and our analytical result is close to recent numerical studies in the literature.

hep-th↗
arXiv2020

Optical theorem and effective action: new proofs of old results in QFT

A new proof of the optical theorem at all orders is presented. Although the theorem is a well-known result in Quantum Field Theory, our proof is interesting because it is particularly simple. Indeed, the theorem is a direct consequence of the pole-ology formalism discussed in Weinberg's Cambridge books. We also discuss a new proof of the standard result concerning the effective action as generating functional of 1PI contributions.

hep-th↗
arXiv2020

Gravitational waves, 100 years later

We present a short communication on the recent direct measurements of gravitational waves, made possible by the joint efforts of the LIGO and the Virgo projects. These notes are devoted to a broad audience. In the first part we will present the basic ideas of the theory of relativity, leading to the prediction of the existence of gravitational waves. The second part is devoted to present the main results and consequences of the discovery.

gr-qc↗
arXiv2019

Quantum quenches, sonic horizons and the Hawking radiation in a class of exactly solvable models

Taking advantage of the known exact mapping of the one-dimensional Hard Core Bose (HCB) fluid onto a non-interacting spinless fermion gas, we examine in full detail a thought experiment on cold atoms confined in a quasi-one-dimensional trap, in order to investigate the emergence of the analogue Hawking radiation. The dynamics of a gas of interacting bosons impinging on an external potential is exactly tracked up to the reach of a stationary state. Under few strict conditions on the experimental parameters, the stationary state is shown to be described asymptotically by a thermal distribution, precisely at the expected (analogue) Hawking temperature. However, we find that in most experimental conditions the emerging `Hawking-like radiation' is not thermal. This analysis provides a novel many-body microscopic interpretation of the Hawking mechanism, together with useful limits and conditions for the design of future experiments in Bose-Einstein condensates.

cond-mat.quant-gas↗
arXiv2019

Non Projected Calabi-Yau Supermanifolds over $\mathbb{P}^2$

We start a systematic study of non-projected supermanifolds, concentrating on supermanifolds with fermionic dimension 2 and with the reduced manifold a complex projective space. We show that all the non-projected supermanifolds of dimension $2|2$ over $\mathbb{P}^2$ are completely characterised by a non-zero 1-form $ω$ and by a locally free sheaf $\mathcal{F}$ of rank $0|2$, satisfying $Sym^2 \mathcal{F} \cong K_{\mathbb{P}^2}$. Denoting such supermanifolds with $\mathbb{P}^{2}_ω(\mathcal{F})$, we show that all of them are Calabi-Yau supermanifolds and, when $ω\neq 0$, they are non-projective, that is they cannot be embedded into any projective superspace $\mathbb{P}^{n|m}$. Instead, we show that every non-projected supermanifolds over $\mathbb{P}^2$ admits an embedding into a super Grassmannian. By contrast, we give an example of a supermanifold $\mathbb P^{2}_ω(\mathcal F)$ that cannot be embedded in any of the $Π$-projective superspaces $\mathbb P^{n}_Π$ introduced by Manin and Deligne. However, we also show that when $\mathcal F$ is the cotangent bundle over $\mathbb{P}^2$, then the non-projected $\mathbb{P}^2_ω(\mathcal F)$ and the $Π$-projective plane $\mathbb P^{2}_Π$ do coincide.

math.AG↗
arXiv2016

Duality invariance in Fayet-Iliopoulos gauged supergravity

We propose a geometric method to study the residual symmetries in $N=2$, $d=4$ $\text{U}(1)$ Fayet-Iliopoulos (FI) gauged supergravity. It essentially involves the stabilization of the symplectic vector of gauge couplings (FI parameters) under the action of the U-duality symmetry of the ungauged theory. In particular we are interested in those transformations that act non-trivially on the solutions and produce scalar hair and dyonic black holes from a given seed. We illustrate the procedure for finding this group in general and then show how it works in some specific models. For the prepotential $F=-iX^0X^1$, we use our method to add one more parameter to the rotating Chow-Compère solution, representing scalar hair.

hep-th↗
arXiv2016

Scattering and delay time for 1D asymmetric potentials: the step-linear and the step-exponential cases

We analyze the quantum-mechanical behavior of a system described by a one-dimensional asymmetric potential constituted by a step plus (i) a linear barrier or (ii) an exponential barrier. We solve the energy eigenvalue equation by means of the integral representation method, classifying the independent solutions as equivalence classes of homotopic paths in the complex plane. We discuss the structure of the bound states as function of the height U_0 of the step and we study the propagation of a sharp-peaked wave packet reflected by the barrier. For both the linear and the exponential barrier we provide an explicit formula for the delay time τ(E) as a function of the peak energy E. We display the resonant behavior of τ(E) at energies close to U_0. By analyzing the asymptotic behavior for large energies of the eigenfunctions of the continuous spectrum we also show that, as expected, τ(E) approaches the classical value for E -> \infty, thus diverging for the step-linear case and vanishing for the step-exponential one.

quant-ph↗