arXiv subjects

Fabrizio Canfora

Publications and source records attributed to Fabrizio Canfora.

At least 37 records · Page 2Linked to original sources

arXiv2025

Fractional vorticity, Bogomol'nyi-Prasad-Sommerfield systems and complex structures for the (generalized) spinor Gross-Pitaevskii equations

The (generalized) Gross-Pitaevskii equation (GPE) for a complex scalar field in two spatial dimensions is analyzed. It is shown that there is an infinite family of self-interaction potentials which admit Bogomol'nyi-Prasad-Sommerfield (BPS) bounds together with the corresponding first-order BPS systems. For each member of this family, the solutions of the first-order BPS systems are automatically solutions of the corresponding second-order generalized GPE. The simplest topologically non-trivial solutions of these first-order BPS systems describe configurations with quantized fractional vorticity. The corresponding fraction is related to the degree of non-linearity. The case in which the self-interaction potential is of order six (namely $|Ψ|^{6}$, which is a relevant theory both in relativistic quantum field theories in $(2+1)$ dimensions in connection with the quantum Hall effect as well as in the theory of the supersolids) is analyzed in detail. Such formalism can also be extended to the case of quantum mixtures with multi-component GPEs. The relationship between these techniques and supersymmetry will be discussed. In particular, despite several common features, we will show that there are multi-component GPEs that are not supersymmetric (at least, not in the standard sense) and possess a BPS system of the above type.

cond-mat.quant-gas↗

arXiv2025

Euclidean AdS wormholes and gravitational instantons in the Einstein-Skyrme theory

Euclidean AdS wormholes provide a natural setup for studying the AdS/CFT correspondence with multiple boundaries. However, from a bottom-up perspective, they cannot be embedded in the four-dimensional Einstein-AdS-Maxwell theory if these boundaries have positive curvature. Nevertheless, Maldacena and Maoz showed that this obstruction could be circumvented by introducing merons in the four-dimensional Einstein-AdS-Yang-Mills theory. In this work, we show that Euclidean-AdS wormholes also exist in the four-dimensional Einstein-AdS-Skyrme theory, whose matter sector possesses a nontrivial baryonic charge. We compute its free energy and show that it does not depend on the integration constants whatsoever, resembling topological solitons. Additionally, we obtain its holographic stress tensor and show that it vanishes, allowing us to interpret this configuration as a holographic Bogomol'nyi-Prasad-Sommerfield (BPS) state. Other topologically nontrivial ground states in Einstein-Skyrme theory are found, such as gravitational instantons, representing the homotopically inequivalent vacua of the theory. We find that they develop Hawking-Page phase transitions above a critical temperature. Some of these solutions are periodic in Euclidean time, representing the gravitational analog of calorons in Yang-Mills theory.

hep-th↗

arXiv2025

Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy

Recently, dynamical edge modes (DEM) in Maxwell theory have been constructed using a specific local boundary condition on the horizon. We discuss how to enforce this boundary condition on an infinite parallel plate in the QED vacuum by introducing Lagrange multiplier fields into the action. We carefully introduce appropriate boundary ghosts to maintain BRST invariance. Explicit correspondence of this BRST extended theory with the original DEM formulation is discussed, both directly, and through the correspondence between edge modes and Wilson lines attached to the boundary surface. We then use functional methods to calculate the Casimir energy for the first time with DEM boundary conditions imposed on two infinite parallel plates, both in generalized Coulomb and linear covariant gauge. Depending on the gauge, different fields are contributing, but, after correctly implementing the BRST symmetry, we retrieve the exact same Casimir energy as for two perfectly conducting parallel plates.

hep-th↗

arXiv2024

Superconducting multi-vortices and a novel BPS bound in chiral perturbation theory

We derive a novel BPS bound from chiral perturbation theory minimally coupled to electrodynamics at finite isospin chemical potential. At a critical value of the isospin chemical potential, a system of three first-order differential field equations (which implies the second-order field equations) for the gauge field and the hadronic profile can be derived from the requirement to saturate the bound. These BPS configurations represent magnetic multi-vortices with quantized flux supported by a superconducting current. The corresponding topological charge density is related to the magnetic flux density, but is screened by the hadronic profile. Such a screening effect allows to derive the maximal value of the magnetic field generated by these BPS magnetic vortices, being $B_{max}=2,04 \times 10^{14}G$. The solution for a single BPS vortex is discussed in detail, and some physical consequences, together with the comparison with the magnetic vortices in the Ginzburg-Landau theory at critical coupling, are described.

hep-th↗

arXiv2024

Exact oscillations and chaos on a non-Abelian coil

We construct new exact solutions of the Georgi-Glashow model in $3+1$ dimensions. These configurations are periodic in time but lead to a stationary energy density and no energy flux. Nevertheless, they possess a characteristic frequency which manifests itself through non-trivial resonances on test fields. This allows us to interpret them as non-Abelian self sustained coils. We show that for larger energies a transition to chaotic behavior takes place, which we characterize by Poincaré sections, Fourier spectra and exponential growth of the geodesic deviation in an effective Jacobi metric, the latter triggered by parametric resonances.

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↗

arXiv2024

Exact mapping from the $(3+1)$-dimensional Skyrme model to the $(1+1)$-dimensional sine-Gordon theory and some applications

A remarkable exact mapping, valid for low-enough energy scales and close to a sharp boundary distribution of hadronic matter, from the $(3+1)$-dimensional Skyrme model to the sine-Gordon theory in $(1+1)$ dimensions in the attractive regime is explicitly constructed. Besides the intrinsic theoretical interest to be able to describe the prototype of nonintegrable theories (namely, quantum chromodynamics in the infrared regime) in terms of the prototype of integrable relativistic field theories (namely, sine-Gordon theory in $(1+1)$ dimensions), we will show that this mapping can be extremely useful to analyze both equilibrium and out-of-equilibrium features of baryonic distributions in a cavity.

hep-th↗

arXiv2023

Gravitating anisotropic merons and squashed spheres in the three-dimensional Einstein-Yang-Mills-Chern-Simons theory

We construct the first analytic examples of self-gravitating anisotropic merons in the Einstein-Yang-Mills-Chern-Simons theory in three dimensions. The gauge field configurations have different meronic parameters along the three Maurer-Cartan $1$-forms and they are topologically nontrivial as the Chern-Simons invariant is nonzero. The corresponding backreacted metric is conformally a squashed three-sphere. The amount of squashing is related to the degree of anisotropy of the gauge field configurations that we compute explicitly in different limits of the squashing parameter. Moreover, the spectrum of the Dirac operator on this background is obtained explicitly for spin-1/2 spinors in the fundamental representation of $SU(2)$, and the genuine non-Abelian contributions to the spectrum are identified. The physical consequences of these results are discussed.

hep-th↗

arXiv2023

Magnetized Baryonic layer and a novel BPS bound in the gauged-Non-Linear-Sigma-Model-Maxwell theory in (3+1)-dimensions through Hamilton-Jacobi equation

It is show that one can derive a novel BPS bound for the gauged Non-Linear-Sigma-Model (NLSM) Maxwell theory in (3+1) dimensions which can actually be saturated. Such novel bound is constructed using Hamilton-Jacobi equation from classical mechanics. The configurations saturating the bound represent Hadronic layers possessing both Baryonic charge and magnetic flux. However, unlike what happens in the more common situations, the topological charge which appears naturally in the BPS bound is a non-linear function of the Baryonic charge. This BPS bound can be saturated when the surface area of the layer is quantized. The far-reaching implications of these results are discussed. In particular, we determine the exact relation between the magnetic flux and the Baryonic charge as well as the critical value of the Baryonic chemical potential beyond which these configurations become thermodynamically unstable.

hep-th↗

arXiv2023

Skyrmions at Finite Density

In this paper, we will describe recent advances in analytical methods to construct exact solutions of the Skyrme model (and its generalizations) representing inhomogeneous Hadronic condensates living at finite Baryon density. Such novel analytical tools are based on the idea to generalize the well known spherical hedgehog ansatz to situations (relevant for the analysis of finite density effects) in which there is no spherical symmetry anymore. Besides the intrinsic mathematical interest to find exact solutions with non-vanishing Baryonic charge confined to a finite volume, this framework opens the possibility to compute important physical quantities which would be difficult to compute otherwise.

hep-th↗

arXiv2023

Partition function of the Potts model on self-similar lattices as a dynamical system and multiple transitions

We present an analytic study of the Potts model partition function on two different types of self-similar lattices of triangular shape with non integer Hausdorff dimension. Both types of lattices analyzed here are interesting examples of non-trivial thermodynamics in less than two dimensions. First, the Sierpinski gasket is considered. It is shown that, by introducing suitable geometric coefficients, it is possible to reduce the computation of the partition function to a dynamical system, whose variables are directly connected to (the arising of) frustration on macroscopic scales, and to determine the possible phases of the system. The same method is then used to analyse the Hanoi graph. Again, dynamical system theory provides a very elegant way to determine the phase diagram of the system. Then, exploiting the analysis of the basins of attractions of the corresponding dynamical systems, we construct various examples of self-similar lattices with more than one critical temperature. These multiple critical temperatures correspond to crossing phases with different degrees of frustration.

cond-mat.stat-mech↗

arXiv2023

Solitonic self-sustained charge and energy transport on the superconducting cylinder

We present an exact time-dependent solution for a charged scalar field on a two-dimensional cylinder, that can be interpreted as representing a long-standing excitation on a $s$-wave superconducting state, which propagates along a nanotube constructed out of twisted bilayer graphene. The solution has a topological charge characterized by an integer number, which counts the winding of the Higgs phase winds around the cylinder. The resulting electric current generates its own electromagnetic field in a self-consistent way, without the need of any external fields to keep it alive.

hep-th↗

arXiv2022

Infinite conformal symmetry and emergent chiral (super)fields of topologically non-trivial configurations: From Yang-Mills-Higgs to the Skyrme model

The present manuscript discusses a remarkable phenomenon concerning non-linear and non-integrable field theories in $(3+1)$-dimensions, living at finite density and possessing non-trivial topological charges and non-Abelian internal symmetries (both local and global). With suitable types of ansätze, one can construct infinite-dimensional families of analytic solutions with non-vanishing topological charges (representing the Baryonic number) labelled by both two integers numbers and by free scalar fields in $(1+1)$-dimensions. These exact configurations represent $(3+1)$-dimensional topological solitons hosting $(1+1)$-dimensional chiral modes localized at the energy density peaks. First, we analyze the Yang-Mills-Higgs model, in which the fields depend on all the space-time coordinates (to keep alive the topological Chern-Simons charge), but in such a way to reduce the equations system to the field equations of two-dimensional free massless chiral scalar fields. Then, we move to the non-linear sigma model, showing that a suitable ansatz reduces the field equations to the one of a two-dimensional free massless scalar field. Then, we discuss the Skyrme model concluding that the inclusion of the Skyrme term gives rise to a chiral two-dimensional free massless scalar field (instead of a free massless field in two dimensions as in the non-linear sigma model) describing analytically spatially modulated Hadronic layers and tubes. The comparison of the present approach both with the instantons-dyons liquid approach and with Lattice QCD is shortly outlined.

hep-th↗

arXiv2022

The Casimir effect in chiral media using path integral techniques

We employ path integral methods to calculate the Casimir energy and force densities in a chiral extension of QED. Manifestly gauge invariant perfect electromagnetic boundary conditions, a natural generalization of perfect electric and perfect magnetic conditions, are implemented directly in the action by the usage of auxiliary fields. The chiral properties of the vacuum are modelled using a background $θ$ field, and we introduce techniques to efficiently calculate the path integral in this chiral medium. The flexibility of our method allows us to naturally obtain results for a variety of configurations, and where comparison is possible our results are in perfect agreement with existing literature. Among these are multiple situations where a repulsive Casimir force is possible.

hep-th↗

arXiv2022

On the robustness of solitons crystals in the Skyrme model

In this work we analize how the inclusion of extra mesonic degrees of freedom affect the finite density solitons crystals of the Skyrme model. In particular, the first analytic examples of hadronic crystals at finite baryon density in both the Skyrme $ω$-mesons model as well as for the Skyrme $ρ$-mesons theory are constructed. These configurations have arbitrary topological charge and describe crystals of baryonic tubes surrounded by a cloud of vector-mesons. In the $ω$-mesons case, it is possible to reduce consistently the complete set of seven coupled non-linear field equations to just two integrable differential equations; one ODE for the Skyrmion profile and one PDE for the $ω$-mesons field. This analytical construction allows to show explicitly how the inclusion of $ω$-mesons in the Skyrme model reduces the repulsive interaction energy between baryons. In the Skyrme $ρ$-mesons case, it is possible to construct analytical solutions using a meron-type ansatz and fixing one of the couplings of the $ρ$-mesons action in terms of the others. We show that, quite remarkably, the values obtained for the coupling constants by requiring the consistency of our ansatz are very close to the values used in the literature to reduce nuclei binding energies of the Skyrme model without vector-mesons. Moreover, our analytical results are in qualitative agreement with the available results on the nuclear spaghetti phase.

hep-th↗

arXiv2022

Analytic meronic black holes, gravitating solitons and higher spins in the Einstein $SU(N)$-Yang-Mills theory

We construct meronic black holes and solitons in the Einstein $SU(N)$-Yang-Mills theory in $D=4$ and $D=5$ dimensions. These analytical solutions are found by combining the generalized hedgehog ansatz with the Euler parameterization of the $SU(N)$ group from which the Yang-Mills equations are automatically satisfied for all values of $N$ while the Einstein equations can be solved analytically. We explicitly show the role that the color number $N$ plays in the black hole thermodynamics as well as in the gravitational spin from isospin effect. Two remarkable results of our analysis are that, firstly, meronic black holes can be distinguished by colored black holes by looking at the spin from isospin effect (which is absent in the latter but present in the former). Secondly, using the theory of non-embedded ansatz for $SU(N)$ together with the spin from isospin effect, one can build fields of arbitrary high spin out of scalar fields charged under the gauge group. Hence, one can analyze interacting higher spin fields in asymptotically flat space-times without "introducing by hand" higher spin fields. Our analysis also discloses an interesting difference between the spin from isospin effect in $D=4$ and in $D=5$.

hep-th↗

arXiv2022

New BPS solitons in N=4 gauged supergravity and black holes in Einstein-Yang-Mills-dilaton theory

We start by revisiting the problem of finding BPS solutions in $\mathcal{N}=4$ SU(2)$\times$SU(2) gauged supergravity. We report on a new supersymmetric solution in the Abelian sector of the theory, which describes a soliton that is regular everywhere. The solution is 1/4 BPS and can be obtained from a double analytic continuation of a planar solution found by Klemm in hep-th/9810090. Also in the Abelian sector, but now for a spherically symmetric ansatz we find a new solution whose supersymmetric nature was overlooked in the previous literature. Then, we move to the non-Abelian sector of the theory by considering the meron ansatz for SU(2). We construct electric-meronic and double-meron solutions and show that the latter also leads to 1/4 BPS configurations that are singular and acquire an extra conformal Killing vector. We then move beyond the supergravity embedding of this theory by modifying the self-interaction of the scalar, but still within the same meron ansatz for a single gauge field, which is dilatonically coupled with the scalar. We construct exact black holes for two families of self-interactions that admit topologically Lifshitz black holes, as well as other black holes with interesting causal structures and asymptotic behavior. We analyze some thermal properties of these spacetimes.

hep-th↗

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↗