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Alessio Marrani

Publications and source records attributed to Alessio Marrani.

At least 19 recordsLinked to original sources
arXiv2026

Integral Orders for the Okubo Algebra and Idempotent Geometries of the $E_8$ Lattice

We study the Coxeter-Dickson $E_8$ order as a common integral support for the octonionic, para-octonionic and compact real Okubo products. The three algebra structures have the same additive lattice, the same positive composition norm and hence the same $240$ norm-one vectors, namely the roots of $E_8$ and the vertices of the Gosset polytope $4_{21}$. Their multiplicative structures are nevertheless different and this difference is already visible in the idempotents: among the same $240$ roots one finds respectively $1$, $57$ and $12$ nonzero integral idempotents. We show that these three counts organize the common root system in three increasingly polarized ways. The octonionic product leaves the full $E_8$ geometry unseparated; the $57$ para-octonionic idempotents reproduce the $E_7$ contact decomposition $1+56+126+56+1$; the $12$ Okubo idempotents split into four mutually orthogonal oriented $A_2$ triangles and hence determine canonically an $A_2^4$ subsystem. Choosing one triangle as the external $A_2$ then yields the $A_2+E_6$ Magic Star, while the remaining nine idempotents determine the trinification subsystem $A_2^3\subset E_6$. This provides an arithmetic interpretation of the $E_8\supset E_7$ and $E_8\supset E_6+A_2$ decompositions directly from integral idempotents.

math.RA↗
arXiv2026

On a new class of high-corank Kac-Moody algebras

We present recursive constructions of several families of generalized Cartan matrices associated with Kac-Moody algebras, whose sizes and coranks grow exponentially. The constructions are encoded by connected multigraphs and by block-doubling operations on their associated symmetric generalized Cartan matrices. Equivalently, the corank problem is translated into a spectral graph-theoretic problem: the corank of $2\mathrm{Id}-\operatorname{Adj}(G)$ is the multiplicity of the adjacency eigenvalue $2$. We give two explicit recursive families, compute their spectra and coranks, and emphasize the difference between absolute exponential growth and relative asymptotic density. The resulting algebras are typically indefinite and singular of corank larger than one, and therefore contain several independent central directions and several isotropic radical directions in the root lattice. We also discuss alternative constructions and possible applications to the algebraic structures appearing in gravity, supergravity, string/M-theory and related generalized symmetry problems.

math.RA↗
arXiv2026

Landau levels via Jordan superalgebras

The goal of this note is to show that Jordan algebras and superalgebras provide an elegant and concise language for formulating quantum mechanical problems with inherent (super)conformal symmetry. The superconformal symmetries of the quantum MICZ-Kepler model and its dual oscillator realization in ${\mathbb R}^2$ are reviewed through the lens of the Tits-Kantor-Koecher correspondence: Kaplansky ${\mathfrak J} {\mathbb R}^{1|2}$ and Exceptional ${\mathfrak J} F^{6|4}$ Jordan superalgebras provide a natural framework for reconstructing (variously extended) superconformal algebras hidden in the Landau levels of an electron in an external magnetic field.

hep-th↗
arXiv2026

Two-time physics, Carroll symmetry and Jordan algebras

We describe Carroll particles with nonzero energy (i.e., particles that remain at rest) within the framework of two-time (2T) physics developed by Bars and collaborators. In a spacetime with one additional time and one additional space dimension, one can gauge the phase-space symmetry that exchanges generalized coordinates with their conjugate momenta, thereby unifying the description of apparently different one-time systems. We develop both classical and quantum descriptions of the Carroll particle arising from 2T physics, and explore links between the extended phase space of 2T physics and Freudenthal triple systems constructed over a semisimple cubic Jordan algebra (the Lorentzian spin factor).

hep-th↗
arXiv2026

Two Times for Freudenthal

We investigate the algebraic structure of the two-time physics introduced some time ago by I. Bars and his co-authors, clarifying its relations with quadratic and cubic Jordan algebras, as well as with reduced Freudenthal triple systems (FTS) based on them. In particular, the `extended' phase space introduced by Bars can be endowed with the structure of a reduced FTS constructed over a semi-simple cubic Jordan algebra (named Lorentzian spin factor), characterized by a primitive, invariant symmetric tensor of rank $4$. The $Sp(2,\mathbb{R})$-gauge fixing procedure typical of two-time physics yields algebraic-differential constraints on the quartic polynomial associated to such a tensor, implying that only two (isomorphic) nilpotent orbits of the non-transitive action of the automorphism group of the Lorentzian spin factor are spanned by the conjugated variables which coordinatize the `extended' phase space. We illustrate our results in relativistic, manifestly Lorentz-covariant physical systems, as well as in non-relativistic systems (such as the non-relativistic massive particle, the hydrogen atom, and the Carroll particle with non-vanishing energy).

hep-th↗
arXiv2026

The Routh of the Attractor Mechanism

We investigate and clarify various aspects of the effective dynamics of Maxwell-Einstein-scalar theories in the background of static, spherically symmetric and asymptotically flat extremal black holes in four space-time dimensions. This rigorously places the one-dimensional effective radial dynamics governed by the Attractor Mechanism, through the critical points of the Ferrara-Gibbons-Kallosh effective black hole potential $V_{BH}$, into the Routhian formalism, a framework which is intermediate between the Lagrange and Hamilton ones, based on a partial Legendre transform, and especially relevant in presence of cyclic variables. We elucidate and analyze the interplay of a trio of effective functionals: the aforementioned $V_{BH}$, Sen's entropy functional $\mathcal{E}$, and the relevant effective Routhian functional $\mathcal{R}$. Through their critical values at the event horizon, such functionals determine the Bekenstein-Hawking and the Wald entropy of the extremal black hole.

hep-th↗
arXiv2025

Lense-Thirring Acoustic Black Holes : Shadows and Light

We introduce the Lense-Thirring Acoustic Black Hole (LTABH), motivated by the relevance of analogue models for black holes embedded in various physical systems, such as the cosmological microwave background or quantum superfluids. We investigate the LTABH spacetime geometry, showing that the roots of the metric function determine a partition of the spacetime into four regions, depending on the acoustic parameter $\xi $ (whereas the dependence vanishes for the rotation parameter $a$); on the other hand, the parameter $a$ turns out to affect the critical radii associated to the maxima of the effective potential. All in all, both the acoustic sphere radius $r_{as}$ and the photon sphere radius $r_{ps}$, respectively giving rise to the acoustic shadow $R_{as}$ and to the optical shadow $R_{s}$, depend on $\xi $ and $a$. More precisely, the rotation parameter $a$ is more relevantly affecting $R_{s}$ (through a right shift), while $R_{as}$ retains its circular shape. For what concerns the acoustic parameter, we notice that the higher $\xi $ is, the larger the size of both shadows. All of these results are confirmed through a detailed analysis of the distortions and of the shadows radii. Moreover, by deriving the magnitude of the precession frequency $\Omega $, we observe that it significantly increases near the acoustic horizons, both in the extremal and in the non-extremal cases, which implies that the Lense-Thirring (frame dragging) effect, which can be traced back to $\xi $ itself, becomes important near such regions. On the other hand, we also show that there are regions of the LTABH spacetime in which $% \Omega $ vanishes, suggesting that therein possible probe particles would not be affected by the frame dragging at all. Finally, we derive the deflection of the light near the LTABH.

gr-qc↗
arXiv2025

Three Dixon-Rosenfeld Planes

Rosenfeld postulated ``generalized'' projective planes, which exploit a correspondence between rank-one idempotents of Jordan algebras $\mathfrak{J}_3(\mathbb{A})$ and points of projective planes $\mathbb{A}P^2$. The isometry groups of the generalized projective planes (which were later defined rigorously as homogeneous spaces) are entries of the Tits-Freudenthal magic square. Given recent interest in the Dixon algebra $\mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$, we extend Rosenfeld's approach and present three new coset manifolds. These "Dixon-Rosenfeld planes" have isometry algebras that are obtained from Tits' magic formula and involve all tensorial components of the Dixon algebra. We show that these are the only three planes obtainable with Tits' formula that preserve the analogy with Rosenfeld's planes. These non-simple Lie algebras generalize $\mathfrak{f}_{4},\mathfrak{e}_{6},\mathfrak{e}_{7}$ and $\mathfrak{e}_{8}$ for the octonionic plane $\mathbb{O}P^{2}$ and in the octonionic Rosenfeld planes $\left(\mathbb{C}\otimes\mathbb{O}\right)P^{2}$, $\left(\mathbb{H}\otimes\mathbb{O}\right)P^{2}$ and $\left(\mathbb{O}\otimes\mathbb{O}\right)P^{2}$. We finally investigate the relationships between the isometry algebras of the Dixon-Rosenfeld planes and the exceptional Lie algebras.

math-ph↗
arXiv2025

New perspectives in Kac-Moody algebras associated to higher dimensional manifolds

In this review, we present a general framework for the construction of Kac-Moody (KM) algebras associated to higher-dimensional manifolds. Starting from the classical case of loop algebras on the circle $\mathbb{S}^{1}$, we extend the approach to compact and non-compact group manifolds, coset spaces, and soft deformations thereof. After recalling the necessary geometric background on Riemannian manifolds, Hilbert bases and Killing vectors, we present the construction of generalized current algebras $\mathfrak{g}(\mathcal{M})$, their semidirect extensions with isometry algebras, and their central extensions. We show how the resulting algebras are controlled by the structure of the underlying manifold, and illustrate the framework through explicit realizations on $SU(2)$, $SU(2)/U(1)$, and higher-dimensional spheres, highlighting their relation to Virasoro-like algebras. We also discuss the compatibility conditions for cocycles, the role of harmonic analysis, and some applications in higher-dimensional field theory and supergravity compactifications. This provides a unifying perspective on KM algebras beyond one-dimensional settings, paving the way for further exploration of their mathematical and physical implications.

hep-th↗
arXiv2025

Linguistic Loops and Geometric Invariants as a Way to Pre-Verbal Thought?

In this work we introduce the concepts of linguistic transformation, linguistic loop and semantic deficit. By exploiting Lie group theoretical and geometric techniques, we define invariants that capture the structural properties of a whole linguistic loop. This result introduces new line of research, employing tools from Lie theory and higher-dimensional geometry within language studies. But, even more intriguingly, our study hints to a mathematical characterization of the meta-linguistic or pre-verbal thought, namely of those cognitive structures that precede the language.

cs.CL↗
arXiv2025

A new method for structural diagnostics with muon tomography and deep learning

This work investigates the production of high-resolution images of typical support elements in concrete structures by means of muon tomography (muography). By exploiting detailed Monte Carlo radiation-matter simulations, we demonstrate the feasibility of reconstructing 1 cm-thick iron bars inside 30 cm-deep concrete blocks, regarded as an important testbed within the structural diagnostics community. In addition, we present a new method for integrating simulated data with advanced deep learning techniques in order to improve the muon imaging of concrete structures. Through deep learning enhancement techniques, this results in a dramatic improvement in image quality and a significant reduction in data acquisition time, which are two critical limitations within the usual practice of muography for civil engineering diagnostics.

hep-ex↗
arXiv2025

Kac-Moody Algebras on Soft Group Manifolds

Within the so-called group geometric approach to (super)gravity and (super)string theories, any compact Lie group manifold $G_{c}$ can be smoothly deformed into a group manifold $G_{c}^{\mu }$ (locally diffeomorphic to $G_{c}$ itself), which is `soft', namely, based on a non-left-invariant, intrinsic one-form Vielbein $\mu $, which violates the Maurer-Cartan equations and consequently has a non-vanishing associated curvature two-form. Within the framework based on the above deformation (`softening'), we show how to construct an infinite-dimensional (infinite-rank), generalized Kac-Moody (KM) algebra associated to $G_{c}^{\mu }$, starting from the generalized KM algebras associated to $G_{c}$. As an application, we consider KM algebras associated to deformed manifolds such as the `soft' circle, the `soft' two-sphere and the `soft' three-sphere. While the generalized KM algebra associated to the deformed circle is trivially isomorphic to its undeformed analogue, and hence not new, the `softening' of the two- and three- sphere includes squashed manifolds (and in particular, the so-called Berger three-sphere) and yields to non-trivial results.

hep-th↗
arXiv2024

Flipped $SU(5)$ GUT with conformal gravity from a single supermultiplet

The Grassmann envelope is used to find the $\mathcal{N}=1$ `superquasiconformal' algebra in $D=10+1$. The adjoint representation of this algebra is found to contain $\mathfrak{su}_{2,2}\oplus \mathfrak{u}_{1}\oplus \mathfrak{su}_{5}$ as a submaximal subalgebra, giving a spectrum of conformal gravity with flipped $SU_{5}\times U_{1}$ GUT. Combining Yang-Mills theory with MacDowell-Mansouri gravity over the conformal group is found to recover the Einstein-Hilbert action with a cosmological constant. An action for the theory is presented, which contains the gauge bosons of gravity and GUT, three generations of fermions in an efficient manner, and a new Higgs sector. By using the superalgebra for the entire multiplet, the theory gauges a non-supersymmetric subalgebra without introducing superpartners.

hep-th↗
arXiv2024

An infinite-rank Lie algebra associated to SL$(2,\mathbb R)$ and SL$(2,\mathbb R)/U(1)$

We construct a generalised notion of Kac-Moody algebras using smooth maps from the non-compact manifolds ${\cal M}=$SL$(2,\mathbb R)$ and ${\cal M}=$ SL$(2,\mathbb R)/U(1)$ to a finite-dimensional simple Lie group $G$. This construction is achieved through two equivalent ways: by means of the Plancherel Theorem and by identifying a Hilbert basis within $L^2(\mathcal{M})$. We analyse the existence of central extensions and identify those in duality with Hermitean operators on $\cal M$. By inspecting the Clebsch-Gordan coefficients of $\mathfrak{sl}(2,\mathbb{R})$, we derive the Lie brackets characterising the corresponding generalised Kac-Moody algebras. The root structure of these algebras is identified, and it is shown that an infinite number of simultaneously commuting operators can be defined. Furthermore, we briefly touch upon applications of these algebras within the realm of supergravity, particularly in scenarios where the scalar fields coordinatize the non-compact manifold $\text{SL}(2,\mathbb{R})/U(1)$.

math-ph↗
arXiv2024

Freudenthal Duality in Conformal Field Theory

Rotational Freudenthal duality (RFD) relates two extremal Kerr-Newman (KN) black holes (BHs) with different angular momenta and electric-magnetic charges, but with the same Bekenstein-Hawking entropy. Through the Kerr/CFT correspondence (and its KN extension), a four-dimensional, asymptotically flat extremal KN BH is endowed with a dual thermal, two-dimensional conformal field theory (CFT) such that the Cardy entropy of the CFT is the same as the Bekenstein-Hawking entropy of the KN BH itself. Using this connection, we study the effect of the RFD on the thermal CFT dual to the KN extremal (or doubly-extremal) BH. We find that the RFD maps two different thermal, two-dimensional CFTs with different temperatures and central charges, but with the same asymptotic density of states, thereby matching the Cardy entropy. We also discuss the action of the RFD on doubly-extremal rotating BHs, finding a spurious branch in the non-rotating limit, and determining that for this class of BH solutions the image of the RFD necessarily over-rotates.

hep-th↗
arXiv2024

Generalized Freudenthal duality for rotating extremal black holes

Freudenthal duality (FD) is a non-linear symmetry of the Bekenstein-Hawking entropy of extremal dyonic black holes (BHs) in Maxwell-Einstein-scalar theories in four space-time dimensions realized as an anti-involutive map in the symplectic space of electric-magnetic BH charges. In this paper, we generalize FD to the class of rotating (stationary) extremal BHs, both in the under- and over-rotating regime, defining a (generalized) rotating FD (generally, non-anti-involutive) map (RFD), which also acts on the BH angular momentum. We prove that the RFD map is unique, and we compute the explicit expression of its non-linear action on the angular momentum itself. Interestingly, in the non-rotating limit, RFD bifurcates into the usual, non-rotating FD branch and into a spurious branch, named "golden" branch, mapping a non-rotating (static) extremal BH to an under-rotating (stationary) extremal BH, in which the ratio between the angular momentum and the non-rotating entropy is the square root of the golden ratio. Finally, we investigate the possibility of inducing transitions between the under- and over-rotating regimes by means of RFD, obtaining a no-go result.

hep-th↗
arXiv2023

Jordan meets Freudenthal. A Black Hole Exceptional Story

Within the extremal black hole attractors arising in ungauged $\mathcal{N}\geqslant 2$-extended Maxwell Einstein supergravity theories in $3+1$ space-time dimensions, we provide an overview of the stratification of the electric-magnetic charge representation space into "large" orbits and related "moduli spaces", under the action of the (continuous limit of the) non-compact $U$-duality Lie group. While each "large" orbit of the $U$-duality supports a class of attractors, the corresponding "moduli space" is the proper subspace of the scalar manifold spanned by those scalar fields on which the Attractor Mechanism is inactive. We present the case study concerning $\mathcal{N}=2$ supergravity theories with symmetric vector multiplets' scalar manifold, which in all cases (with the exception of the minimally coupled models) have the electric-magnetic charge representation of $U$-duality fitting into a reduced Freudenthal triple system over a cubic (simple or semi-simple) Jordan algebra.

hep-th↗