arXiv subjects

Federico Manzoni

Publications and source records attributed to Federico Manzoni.

11 recordsLinked to original sources

arXiv2026

The Zak phase in topologically insulating chains: invariants and limitations

In this work we investigate the topological content of the Zak phase in one-dimensional translation-invariant topological insulators endowed with time-reversal, particle-hole and/or chiral symmetries, extending results from \cite{Monaco_2023}. We analyze the extent to which the Zak phase captures the topology of all Altland--Zirnbauer--Cartan (AZC) symmetry classes in $1$D. Building on the framework of fibered Hamiltonians and spectral projections, we construct symmetric Bloch bases adapted to the discrete symmetries of the system and define a $\mathbb{Z}_2$-valued topological invariant $\mathrm{I}^{(\mathrm{AZC-class})}(H)$ obtained from the abelian Zak phase. Moreover, we demonstrate that in symmetry classes admitting a quaternionic structure, i.e. anti-unitary symmetries squaring to minus the identity, the Zak phase is further constrained, leading to the vanishing of the $\mathbb{Z}_2$ invariant mentioned above. This highlights the sensitivity of the Zak phase to additional geometric structures of the manifold of occupied energy states, as well as its limitations in being an effective marker for topological phases of insulating chains. As an example, we discuss the case of generalized Kitaev chains with arbitrary finite-range hopping and single or multiple chiral channels, and show how the Zak phase only retains partial information about their different topological phases.

math-ph↗

arXiv2026

The asymptotic charges of Curtright dual graviton and Curtright extensions of BMS algebra

This paper studies the asymptotic gauge charges of the Curtright mixed-symmetry rank-3 field $\phi_{[\rho\sigma]\nu}$ in Minkowski spacetime, interpreted in $ D = 5 $ as the dual graviton. In Bondi coordinates at future null infinity, we impose radiation fall-offs and fix a de Donder-like gauge together with an on-shell traceless condition, similarly to what happens in linearized gravity. Surface charges associated with the residual gauge transformations are constructed as boundary integrals via N\"other's 2-form. In $ D = 5 $, exploiting Hodge/Hodge-like decompositions on $ S^{3} $, the charge splits into a scalar sector $ Q_{\Phi} $, a vector sector $ Q_{V} $ and a TT sector $Q_{y^{\text{TT}}}$. $ Q_{\Phi} $ is parametrized by a single arbitrary scalar function $ \Phi $ (interpreted as the supertranslation-like parameter), $ Q_{V} $ is parametrized by a vector field $ V^{i} \in \mathfrak{Diff}(S^{3}) $ and the TT sector $Q_{y^{\text{TT}}}$ is parametrized by a trasverse-traceless rank-2 tensor $y_{ij}^{\text{TT}} \in \mathfrak{TT}(S^3)$. The corresponding charge algebra closes only if $V_i \in \mathfrak{o}(4)$ as semidirect sum generating an abelian extension of a $\mathfrak{BMS}$-like algebra featuring a higher-spin-like supertranslation sector.

hep-th↗

arXiv2025

Higher-order $p$-form asymptotic symmetries in $D = p + 2$

We investigate higher-order asymptotic symmetries for a $p$-form gauge field in $(p + 2)$-dimensional Minkowski spacetime, where Hodge duality with a scalar holds. Employing symplectic renormalization, we identify $N + 1$ independent asymptotic charges, with each charge being parametrised by an arbitrary function of the angular variables. By means of the Hodge decomposition, these charges share the same formal structure independently from p and are manifestly dual to a scalar charge. We work in Lorenz gauge, therefore the gauge parameters require a radial expansion involving logarithmic (subleading) terms to ensure nontrivial angular dependence at leading order. At the same time we assume a power expansion for the field strength, allowing logarithms in the gauge field expansions within pure gauge sectors.

hep-th↗

arXiv2025

On the solution of the harmonic-divgrad PDEs system

We study a particular system of partial differential equations in which the Laplace--Beltrami, the divergence and the gradient operators of the unknown functions appear (harmonic-divgrad system). Using the Killing--Hopf theorem and leveraging the properties of Riemannian manifolds with constant sectional curvature we establish the conditions under which these equations admit only the trivial solutions proving their trivialization on positive curvature space forms. The analysis of this particular system is motivated by its occurrence in the study of asymptotic symmetries in $p$-form gauge theories and in mixed symmetry tensor gauge theories.

math-ph↗

arXiv2025

Duality, asymptotic charges and algebraic topology in mixed symmetry tensor gauge theories and applications

Recently the duality map between electric-like asymptotic charges of $p$-form gauge theories is studied. The outcome is an existence and uniqueness theorem and the topological nature of the duality map. The goal of this work is to extend that theorem in the case of mixed symmetry tensor gauge theories in order to have a deeper understanding of exotic gauge theories, of the non-trivial charges associated to them and of the duality of their observables. Unlike the simpler case of $p$-form gauge theories, here we need to develop some mathematical tools. The crucial points are to view a mixed symmetry tensor as a Young projected object of the $N$-multi-form space and to develop an analogue of de Rham complex for mixed symmetry tensors. As a result, if the underlying manifold satisfy appropriate conditions, the duality map can be proven to exist and to be unique ensuring the charge of a description has information on the dual ones. Moreover, we provide some physical applications ranging form fractons and higher symmetries to string theory and holography.

math-ph↗

arXiv2024

2-simplexes and superconformal central charges

The superconformal central charge is an important quantity for theories emerging from string theory geometrical implementation of Quantum Field Theory since it is linked, for example, to the scaling dimension of fields. Butti and Zaffaroni construction of the central charge for toric Calabi-Yau threefold geometries is a powerful tool but its implementation could be quite tricky. Here we present an equivalent new construction based on a 2-simplexes decomposition of the toric diagram.

hep-th↗

arXiv2024

Duality, asymptotic charges and higher form symmetries in $p$-form gauge theories

The surface charges associated with $p$-form gauge fields in the Bondi patch of $D$-dimensional Minkowski spacetime are computed. We show that, under the Hodge duality between the field strengths of the dual formulations, electric-like charges for $p$-forms are mapped to magnetic-like charges for the dual $q$-forms, with $q=D-p-2$. We observe that the complex combination of electric-like and magnetic-like charges transforms under duality according to a specific M\"obius transformation. This leads to a possible construction of CCFT in $D=4$ as a M\"obius-principal equivariant bundle, together with its associated bundles, in order to recover celestial operators. We prove an existence and uniqueness theorem for the duality map relating the asymptotic electric-like charges of the dual descriptions, and we provide an algebraic-topological interpretation of this map. As a result, the duality map has a topological nature and ensures that the charge of one formulation contains information about the dual formulation, leading to a deeper understanding of gauge theories, the non-trivial charges associated with them, and the duality of their observables. Moreover, we propose a link between higher-form symmetry charges, naturally associated with a $p$-form gauge theory, and their asymptotic charges. The higher-form charges are reproduced by choosing the gauge parameter to be constant and supported only on an appropriate codimension submanifold. This could partially answer an open question in the celestial holography program.

math-ph↗

arXiv2024

Asymptotic charges of $p-$forms and their dualities in any $D$

We compute the surface charges associated to $p-$form gauge fields in arbitrary spacetime dimension for large values of the radial coordinate. In the critical dimension where radiation and Coulomb falloff coincide we find asymptotic charges involving asymptotic parameters, i.e. parameters with a component of order zero in the radial coordinate. However, in different dimensions we still find nontrivial asymptotic charges now involving parameters that are not asymptotic times the radiation-order fields. For $p$=1 and $D>4$, our charges thus differ from those presented in the literature. We then show that under Hodge duality electric charges for $p-$forms are mapped to magnetic charges for the dual $q-$forms, with $q = D-p-2$. For charges involving fields with radiation falloffs the duality relates charges that are finite and nonvanishing. For the case of Coulomb falloffs, above or below the critical dimension, Hodge duality exchanges overleading charges in one theory with subleading ones in its dual counterpart.

hep-th↗

arXiv2024

Axialgravisolitons at infinite corners

Gravitational solitons (gravisolitons) are particular exact solutions of Einstein field equation in vacuum build on a given background solution. Their interpretation is not yet fully clear but they contain many of the physically relevant solutions low $N$-solitons solutions. However, a systematic study and characterization of gravisolitons solution for every $N$ is lacking and their relevance in a theory of quantum gravity is not fully understood. This work aims to investigate and characterize some properties of $N$-axialsoliton solutions such as their asymptotically behaviour and asymptotic symmetries given minimal assumptions on the background metric. We develop an explicit systematic asymptotically expansion for the $N$-axialsoliton solution and we compute the leading order of the asymptotic killing vectors. Moreover, in the perspective to better understand the role of gravisolitons in quantum gravity we make a link, and a one of the first explicit test, to the corner symmetry proposal deriving which subalgebra of the universal corner symmetry algebra is generated by the asymptotic Killing vectors of $N$-axialsoliton solution. In the spirit of the corner proposal, the axialgravisoliton corner symmetry algebra (\textfrak{agcsa}) can be useful for the quantization of the non-asymptotically flat sector of gravity while, in the spirit of IR triangle, new soft theorems and memory effects could emerge.

gr-qc↗

arXiv2024

Algebro-geometrical orientifolds and IR dualities

Orientifold projections are an important ingredient in geometrical engineering of Quantum Field Theory. However, an orientifold can break down the superconformal symmetry and no new superconformal fixed points are admitted (II scenario); nevertheless, in some cases, dubbed I and III scenarios orientifold, a new IR fixed point is achieved and, for III scenario examples, some still not fully understood IR duality seems to emerge. Here we give an algebro-geometrical point of view of III scenario orientifold for toric varieties and we propose the existence of relevant operators that deform the starting oriented CFT triggering a flow. We briefly discuss a possible holographic description of this flow.

hep-th↗

arXiv2022

Solitonic solutions and gravitational solitons: an overview

In this work we intend to discuss the solitonic solutions of Einstein's field equations in vacuum by constructing the solution to N solitons and studying some aspects of it. In conclusion, it will be shown how the Kerr black hole can be interpreted as a soliton solution in the case of axial symmetry.

nlin.SI↗