arXiv subjects

Jorge Zanelli

Publications and source records attributed to Jorge Zanelli.

At least 19 recordsLinked to original sources

arXiv2026

Chiral symmetry breaking in models with unconventional supersymmetry

We investigate dynamical mass generation in a geometrically constructed gauge theory based on the super Lie algebra $su(2,2|3)$, in which gravity, Yang-Mills fields, and fermions are unified as components of a single gauge connection. The model contains no elementary scalar fields and no ad hoc four-fermion interactions. Instead, fermionic self-interactions arise unavoidably from the geometric structure of the theory, through nonminimal couplings and torsion associated with the unified connection. Upon reduction to an effective low-energy description, these interactions generate a Nambu-Jona-Lasinio--type potential that triggers chiral symmetry breaking and the formation of a fermion mass gap. In this framework, mass generation emerges as a direct consequence of the underlying gauge-geometric and algebraic structure, rather than as an independent dynamical assumption.

hep-th↗

arXiv2025

(3+1)-dimensional compressible fluid as a (4+1)-dimensional Chern-Simons system

A fluid described by an Abelian Chern-Simons action principle in 4+1 dimensions is considered. Letting 3+1 dimensions correspond to the usual space and time, and assuming the fields to be independent of the fifth coordinate, the free theory provides an interpretation as a system of advection equations, where the advecting velocity field is defined as the null vector of the field strength tensor (curvature). The free theory possesses a number of conservation laws which turn out to be prototypical forms of helicity and entropy conservation. Coupling the Chern-Simons field to an external source, a new conserved charge density is obtained which has the form of the Rossby-Ertel's potential vorticity (PV). Finally, by identifying the external current with the Chern-Simons field in a gauge-invariant setting, based on non-relativistic ideas, a self-interacting action principle is obtained whose Euler-Lagrange equations correspond precisely to a classical dissipationless compressible (3+1)-dimensional fluid endowed with thermodynamics, with only one extra condition: a constraint on the initial profile of the PV. After analysing this constraint of the "Chern-Simons fluid formulation", we investigate the helicity conservation of general fluids, going beyond classical analyses of barotropic fluids and no-cross boundary conditions for vorticity (Moffatt 1969). A new fluid helicity invariant for barotropic fluids under generic boundary conditions is obtained and the role of baroclinity in the helicity production is clarified. Inside a region bounded by an isentropic surface, the theory's constraint on the PV gives an integral formula for the mass, and for the evolution of fluid helicity in the baroclinic case. Finally, for an ideal gas exact, steady solutions of the equations of motion are found in a rotating scenario, showing that Ferrel-cell like patterns are produced in a rotating planet.

physics.flu-dyn↗

arXiv2025

BPS defects in AdS$_{3}$ supergravity

AdS supergravity admits supersymmetric solutions that describe BPS defects. Here, we investigate such solutions in AdS$_3$ supergravity, which is formulated as a Chern-Simons theory on $\mathrm{OSp}(2|1)\,\times\, \mathrm{OSp}(2|1)$. We compute the Killing spinor equation on the BTZ geometry in different ways, looking for BPS solutions on the entire space of parameters. We focus our attention on defects that represent geometries with integer angular excesses; these correspond to specific negative values of the BTZ mass. We compare our solutions with other results in the literature, finding exact agreement. We argue that, in the semiclassical limit, the BPS defects can be associated to degenerate representations of the Virasoro symmetry at the boundary. The case of non-diagonal representations, describing stationary, non-static defects, is also discussed.

hep-th↗

arXiv2024

BPS states in AdS$_3$ Supergravity with Chiral Torsion

In this letter, we construct a supersymmetric model, obtained by deforming $\mathcal N=2$ AdS$_3$ supergravity through a chiral vector component of the torsion. Moreover, we study the existence of BPS states of such theory, by inspecting the presence of Killing spinors on a specific bosonic solution.

hep-th↗

arXiv2024

On the central singularity of the BTZ geometries

The nature of the central singularity of the BTZ geometries -- stationary vacuum solutions of 2+1 gravity with negative cosmological constant $Λ=-\ell^{-2}$ and $SO(2)\times \mathbb{R}$ isometry -- is discussed. The essential tool for this analysis is the holonomy operator on a closed path (i.e., Wilson loop) around the central singularity. The study considers the holonomies for the Lorentz and AdS$_3$ connections. The analysis is carried out for all values of the mass $M$ and angular momentum $J$, namely, for black holes ($M \ell \ge |J|$) and naked singularities ($M \ell < |J|$). In general, both Lorentz and AdS$_3$ holonomies are nontrivial in the zero-radius limit revealing the presence of delta-like singularity at the origin in the curvature and torsion two-forms. However, in the cases $M\pm J/\ell=-n_{\pm}^2$, with $n_{\pm} \in \mathbb{N}$, recently identified in \cite{GMYZ} as BPS configurations, the AdS$_3$ holonomy reduces to the identity. Nevertheless, except for the AdS$_{3}$ spacetime ($M=-1$, $J=0$), all BTZ geometries have a central singularity which is not revealed by local operations.

gr-qc↗

arXiv2024

Massless Rarita-Schwinger equations: Half and three halves spin solution

Counting the degrees of freedom of the massless Rarita-Schwinger theory is revisited using Behrends-Fronsdal projectors. The identification of the gauge invariant part of the vector-spinor is thus straightforward, consisting of spins 1/2 and 3/2. The validity of this statement is supported by the explicit solution found in the standard gamma-traceless gauge. Since the obtained systems are deterministic -- free of arbitrary functions of time -- we argue that the often-invoked residual gauge symmetry lacks fundamental grounding and should not be used to enforce new external constraints. The result is verified by the total Hamiltonian dynamics. We conclude that eliminating the spin-12 mode \textit{via} the extended Hamiltonian dynamics would be acceptable if the Dirac conjecture was assumed; however, this framework does not accurately describe the original Lagrangian system.

hep-th↗

arXiv2024

Inflation and late-time accelerated expansion driven by $k$-essence degenerate dynamics

We consider a k-essence model in which a single scalar field can be responsible for both primordial inflation and the present observed acceleration of the cosmological background geometry, while also admitting a nonsingular de Sitter beginning of the Universe (it arises from de Sitter and ends in de Sitter). The early one is driven by a slow-roll potential, and the late one is driven by a dynamical dimensional reduction process which freezes the scalar field in a degenerate surface, turning it into a cosmological constant. This is done by proposing a realizable stable cosmic time crystal, although giving a different interpretation to the ''moving ground stat'', in which there is no motion because the system loses degrees of freedom. Furthermore, the model is free of pathologies such as propagating superluminal perturbations, negative energies, and perturbation instabilities.

hep-th↗

arXiv2023

Self duality in unconventional conformal supersymmetry

In this work, we study (anti-)self duality conditions in unconventional conformal supersymmetry. We focus on a theory constructed in a Townsend-MacDowell-Mansouri form for an $SU(2,2|N)$ gauge connection with matter fields in the adjoint representation. We found bosonic solutions that correspond to analytic gravitational instantons with nontrivial torsion. These configurations can be regarded as the torsional generalization of the Taub-NUT/Bolt-AdS and Eguchi-Hanson metric and they are (anti-)self-dual with respect to a generalized dual operator. We explore their global properties and show that they saturate a BPS bound.

hep-th↗

arXiv2023

New Torsional Deformations of Locally AdS$_3$ Space

We consider general torsion components in three-dimensional Einstein-Cartan gravity, providing a geometrical interpretation for matter, and find new solutions of the corresponding equations for the Riemann curvature and torsion. These geometries involve a peculiar interplay between the vector $(β_i)$ and the singlet $(τ)$ irreducible components of the torsion which, under general conditions, feature a formal analogy with the equation for a Beltrami fluid. Interestingly, we find that the local AdS$_3$ geometry is now deformed by effect of the "Beltrami-torsion" $β_i$. Some of these new solutions describe deformations of the BTZ black hole due to the presence of torsion. The latter acts as a geometric flux which, in some cases, removes the causal singularity.

hep-th↗

arXiv2023

On the spin content of the classical massless Rarita--Schwinger system

We analyze the Rarita--Schwinger (RS) massless theory in the Lagrangian and Hamiltonian approaches. At the Lagrangian level, the standard gamma-trace gauge fixing constraint leaves a spin-1/2 and a spin-3/2 propagating Poincaré group helicities. At the Hamiltonian level, the result depends on whether the Dirac conjecture--that all first class constraints generate gauge symmetries--is assumed or not. In the affirmative case, a secondary first class constraint must be added to the total Hamiltonian and a corresponding gauge fixing condition must be imposed, completely removing the spin-1/2 sector. In the opposite case, the spin-1/2 field propagates and the Hamilton field equations match the Euler-Lagrange equations.

hep-th↗

arXiv2023

Quantum backreaction for overspinning BTZ geometries

We examine the semiclassical backreaction of a conformally coupled scalar field on an overspinning BTZ geometry. This extends the work done on a similar problem for ($2+1$)- AdS geometries of the BTZ family with $|M|>|J|$. The overspinning classical solutions corresponds to $|M|<|J|$ and possess a naked singularity at $r=0$. Using the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such a spacetime, we obtain the semiclassical Einstein equations, which we attempt to solve perturbatively. We show that the stress-energy tensor is non-renormalizable in this approach, and consequently the perturbative solution to the semiclassical equations in the overspinning case does not exist. This could be an indication of the fact that the naked singularity at the center of an overspinning geometry is of a more severe nature than the conical singularity found in the same family of BTZ geometries.

hep-th↗

arXiv2022

Simplified Two-Dimensional Model for Global Atmospheric Dynamics

We present a simplified model of the atmosphere of a terrestrial planet as an open two-dimensional system described by an ideal gas with velocity $\vec{v}$, density $ρ$ and temperature $T$ fields. Starting with the Chern-Simons equations for a free inviscid fluid, the external effects of radiation and the exchange of matter with the strata, as well as diffusion and dissipation are included. The resulting dynamics is governed by a set of nonlinear differential equations of first order in time. This defines an initial value problem that can be integrated given the radiation balance of the planet. If the nonlinearities are neglected, the integration can be done in analytic form using standard Green function methods, with small nonlinearities incorporated as perturbative corrections in a consistent way. If the nonlinear approximation is not justified, the problem can be integrated numerically. The analytic expressions as well as the simulations of the linear regime for a continuous range of parameters in the equations is provided, which allows to explore the response of the model to changes of those parameters. In particular, it is observed that a 2.5% reduction in the emissivity of the atmosphere can lead to an increase of 7C degrees in the average global temperature.

physics.ao-ph↗

arXiv2022

A black hole solution in conformal supergravity

We present a three-parameter family of analytic black-hole solutions in the bosonic sector of a four-dimensional supersymmetric model with matter fields in the adjoint representation. The solutions are endowed with curvature and torsional singularities which are both surrounded by an event horizon. They are asymptotically Lorentz flat, representing the torsional generalization of the Riegert black hole in conformal gravity. We compute the partition function to first order in the saddle-point approximation which turns out to be finite without any reference to boundary counterterms. We find a non-maximmally symmetric thermalized ground state, whose existence is relevant when studying Hawking-Page phase transitions. Finally, we discuss future directions regarding its extended phase space.

hep-th↗

arXiv2022

Embedding of the Georgi-Glashow $SU(5)$ model in the superconformal algebra

We present a scheme to construct grand unified models based on the superconformal algebra and the inclusion of matter fields in the adjoint representation of supersymmetry. As an illustration, we implemented the Georgi-Glashow $SU(5)$ model. The model predics the existence of a hidden $(\mathbf{1},\mathbf{24},0) + (\mathbf{5},\mathbf{5}^\ast,-y') + (\mathbf{5}^\ast,\mathbf{5},y')$ sector and an anomalous $U(1)_Z$.

hep-th↗

arXiv2022

Electric/Magnetic Newton-Hooke and Carroll Jackiw-Teitelboim Gravity

We construct the electric and magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity theories using the isomorphism of Newton-Hooke$_\pm$ and (A-)dS Carroll algebras in $(1+1)$-spacetime dimensions. The starting point is the non-relativistic and Carroll version of Jackiw-Teitelboim gravity without restrictions on the geometry studied in [15].

hep-th↗

arXiv2022

Dynamical dimensional reduction in multi-valued Hamiltonians

Several interesting physical systems, such as the Lovelock extension of General Relativity in higher dimensions, classical time crystals, k-essence fields, Horndeski theories, compressible fluids, and nonlinear electrodynamics, have apparent ill defined sympletic structures, due to the fact that their Hamiltonians are multi-valued functions of the momenta. In this paper, the dynamical evolution generated by such Hamiltonians is described as a degenerate dynamical system, whose sympletic form does not have a constant rank, allowing novel features and interpretations not present in previous investigations. In particular, it is shown how the multi-valuedness is associated with a dynamical mechanism of dimensional reduction, as some degrees of freedom turn into gauge symmetries when the system degenerates.

hep-th↗

arXiv2021

Degeneracy Index and Poincaré-Hopf Theorem

A degenerate dynamical system is characterized by a state-dependent multiplier of the time derivative of the state in the time evolution equation. It can give rise to Hamiltonian systems whose symplectic structure possesses a non-constant rank throughout the phase space. Around points where the multiplier becomes singular, flow can experience abrupt and irreversible changes. We introduce a topological index for degenerate dynamical systems around these {\it degeneracy points} and show that it refines and extends the usual topological index in accordance with the Poincaré-Hopf Theorem.

math-ph↗

arXiv2021

$\mathcal{N}=2$ Extended MacDowell-Mansouri Supergravity

We construct a gauge theory based in the supergroup $G=SU(2,2|2)$ that generalizes MacDowell-Mansouri supergravity. This is done introducing an extended notion of Hodge operator in the form of an outer automorphism of $su(2,2|2)$-valued 2-form tensors. The model closely resembles a Yang-Mills theory -- including the action principle, equations of motion and gauge transformations -- which avoids the use of the otherwise complicated component formalism. The theory enjoys $H=SO(3,1)\times \mathbb{R} \times U(1)\times SU(2)$ off-shell symmetry whilst the broken symmetries $G/H$, translation-type symmetries and supersymmetry, can be recovered on surface of integrability conditions of the equations of motion, for which it suffices the Rarita-Schwinger equation and torsion-like constraints to hold. Using the \textit{matter ansatz} -- projecting the $1 \otimes 1/2$ reducible representation into the spin-$1/2$ irreducible sector -- we obtain (chiral) fermion models with gauge and gravity interactions.

hep-th↗