arXiv subjects

P. D. Alvarez

Publications and source records attributed to P. D. Alvarez.

6 recordsLinked to original sources

arXiv2026

Gravity and Matter from Soldered Chiral Superconnections

We present a reformulation of four-dimensional chiral gravity in terms of a chiral gauge connection and a Clifford-valued coframe. The exterior algebra generated by $e^a \gamma_a$, together with the gauge curvature $F$, provides a natural and systematic construction of gauge-covariant differential forms. We show that suitable combinations of the chiral actions reproduce Einstein--Cartan--Holst gravity with a cosmological term. The original superconnection invariants yield only algebraic fermionic equations, so the fermionic one-forms do not propagate but instead generate a mass-like mixing between the two chiralities. Spinor propagation is supplied by a spinorial BF-type term, which under the matter ansatz reduces to the standard first-order Weyl kinetic action, including the torsion coupling. We also review the symmetry and variational properties of the matter ansatz, including its Lorentz equivariance, its relation to residual supersymmetry and twistor spinors, and the connection between the reduced and unrestricted field equations.

hep-th↗

arXiv2026

Variations on a theme of MacDowell-Mansouri

Inspired by the MacDowell-Mansouri formulation of four-dimensional General Relativity, we study a class of four-dimensional gauge-theoretic functionals obtained from the Pontryagin density of a G-connection by inserting, under the trace, a matrix that breaks the gauge group G to a subgroup H. Concretely, we study the model with the pair (G,H) given by (SU(3), U(2)). We show that the critical points of the resulting functional are constant scalar curvature almost-Kahler 4-manifolds. On compact 4-manifolds, a stronger conclusion holds under the additional assumption that the scalar curvature is non-negative and the first Chern class is such that an Einstein metric can exist. In this case, results in the literature imply that the critical points are Kahler-Einstein 4-manifolds.

math.DG↗

arXiv2025

Gravitating spinor torsional BTZ solution

We construct exact analytic solutions for a supersymmetric Chern-Simons theory with matter fields in the adjoint representation (unconventional supersymmetry). The configurations correspond to gravitating spinor fields on BTZ geometries with torsion. Although the spinor profiles exhibit divergent behavior near the black hole horizon, they yield finite contributions to conserved charges. We demonstrate that the spinors solve the full nonlinear field equations and satisfy integrability conditions derived from the Bianchi identities. The resulting energy momentum tensor is traceless, consistent with the Weyl invariance of the theory. We also analyze spinor solutions based on $adS_3$ Killing spinors and identify the conditions under which such backgrounds can support nontrivial spinor configurations. Our findings open the way to new fermionic sectors in 3D gravity with torsion, distinct from previously known perturbative deformations.

hep-th↗

arXiv2022

Gauging the superconformal group with a graded dual operator

Based on the superconformal algebra we construct a dual operator that introduces a grading among bosonic generators independent of the boson/fermion grading of the superalgebra. This dual operator allows us to construct an action that is gauge invariant under the grading even bosonic generators. We provide a self-dual notion based on the dual operator. We use the definition of the dual operator to contruct a model with gauge invariance $SO(1,3)\times SU(N) \times U(1) \subset SU(2,2|N)$. The choice of a graded dual operator allows us to overcome technical difficulties of $U(N)$ unified theories based on the superconformal group. The gravity action reproduces the Einstein-Hilbert action in certain sector of the theory. The definition of the dual operator allows us to include fermionic matter in the gauge connection in a geometric manner. We give a summary with possible phenomenological parameters that are included in the model.

hep-th↗

arXiv2017

Testing a new WISP Model with Laboratory Experiments

We explore the phenomenological consequences of a model with axion-like particles and hidden photons mixing with photons. In this model, the hidden photon is directly coupled to the photon, while the axion coupling is induced by an external electromagnetic field. We consider vacuum effects on a polarised photon beam, like changes in the ellipticity and rotation angles.

hep-ph↗

arXiv2017

Integrability and chemical potential in the (3+1)-dimensional Skyrme model

Using a remarkable mapping from the original (3+1)dimensional Skyrme model to the Sine-Gordon model, we construct the first analytic examples of Skyrmions as well as of Skyrmions--anti-Skyrmions bound states within a finite box in 3+1 dimensional flat space-time. An analytic upper bound on the number of these Skyrmions--anti-Skyrmions bound states is derived. We compute the critical isospin chemical potential beyond which these Skyrmions cease to exist. With these tools, we also construct topologically protected time-crystals: time-periodic configurations whose time-dependence is protected by their non-trivial winding number. These are striking realizations of the ideas of Shapere and Wilczek. The critical isospin chemical potential for these time-crystals is determined.

hep-th↗