arXiv subjects

J. Lorca Espiro

Publications and source records attributed to J. Lorca Espiro.

10 recordsLinked to original sources

arXiv2026

Emergence of Dark Energy from topology and chiral spinors

Under the existence of a massless spinor with respect to the total connection in a spacetime modeled as a Lorentzian manifold with internal boundaries, such as finite volume semi-classical Black Holes, we show that a topological mechanism naturally induces terms in the Einstein-Cartan gravitational action that can be interpreted as General Relativity with dark energy. This may alleviate the problems of dark energy. The topological information is carried by a harmonic 1-form associated to the first co-holomology group of the spacetime, which induces a spacetime contortion acting on the horizontal bundle.

gr-qc↗

arXiv2025

Non-Abelian fusion rules from Abelian systems with SPT phases and graph topological order

Since Ref. [1] shows the emergence of non-Abelian fusion rules in some examples of a class of Abelian models, but does not prove whether these rules also exist in other cases, the purpose of this paper is to present such proof emphasizing the importance of the existence of these rules. By the way, as the ground state of these models can be degenerate as a function of their algebra and, hence, they can support some symmetry-protected topological (SPT) phases, we prove that these non-Abelian fusion rules are always necessary for these SPT phase transitions to occur via a condensation mechanism or/and some global symmetry breaking.

quant-ph↗

arXiv2024

A dualization approach to the Ground State Subspace Classification of Abelian Higher Gauge Symmetry Models

In the literature, abelian higher gauge symmetry models are shown to be valid in all finite dimensions and exhibit the characteristic behavior of SPT phases models. While the ground state degeneracy and the entanglement entropy were thoroughly studied, the classification of the ground state space still remained obscure. Based on differentio-geometric approach and, anticipating the notation of the current paper, if $\left( C_{\bullet} , \partial^C_{\bullet} \right)$ is the chain complex associated to the geometrical content of these models, while $\left( G_{\bullet} , \partial^G_{\bullet} \right)$ is its symmetries counterpart, we show that the ground state space is classified by a $H^0 (C,G) \times H_0 (C,G)$ group, where $H^0(C,G)$ is the $0$-th cohomology and $H_0 (C,G)$ is the corresponding $0$-th homology group with coefficients in the chain complex.

math-ph↗

arXiv2023

Quantum Double Models coupled to matter fields: a detailed review for a dualization procedure

In this paper, we investigate how it is possible to define a new class of lattice gauge models based on a dualization procedure of a previous generalization of the Kitaev Quantum Double Models. In the case of this previous generalization that will be used as a basis, it was defined by adding new qudits (which were denoted as matter fields in reference to some works) to the lattice vertices with the intention of, for instance, interpreting its models as Kitaev Quantum Double Models coupled with Potts ones. Now, with regard to the generalization that we investigate here, which we want to define as the dual of this previous one, these new qudits were added to the lattice faces. And as the coupling between gauge and matter qudits of the previous generalization was performed by a gauge group action, we show that the dual behaviour of these two generalizations was achieved by coupling these same qudits in the second one through a gauge group co-action homomorphism. One of the most striking dual aspects of these two generalizations is that, in both, part of the quasiparticles that were inherited from the Kitaev Quantum Double Models become confined when these action and co-action are non-trivial. But the big news here is that, in addition to the group homomorphism (that defines this gauge group co-action) allows us to classify all the different models of this second generalization, this same group homomorphism also suggests that all these models can be interpreted as two-dimensional restrictions of the $ 2 $-lattice gauge theories.

quant-ph↗

arXiv2020

Is the Cosmological Constant of Topological Origin?

The observed value of the cosmological constant poses large theoretical problems. We find that topology of the Universe provides a natural source for it. Restricting dynamically an Einstein-Cartan gravity to General Relativity in our observed Universe allows topological invariants to induce an effective cosmological constant from dynamical quintessence-like topological fields. Its evaluation through the boundary of black holes yields a range compatible with the observed value, with uncertainty of three orders of magnitude. In turns, it provides a measurement of the Universe's isoperimetric constant.

gr-qc↗

arXiv2019

Dark Energy from Topology

The concordance model of cosmology suffers from the major theoretical problems surrounding the observed value and recent emergence of a cosmological constant. In this paper we present a novel approach, which explains more naturally its value than that based on quantum vacuum energy, in the form of topological invariants characteristic classes, included as Lagrange multipliers in the action. The approach draws from topological as well as dynamical system consideration, generating as a byproduct an effective cosmological constant. General Relativity is recovered by canceling the torsion in a region containing the observable Universe, which boundary constraints the invariants, thus yielding the effective cosmological constant's form. As that form's denominator contains the total volume of the average black hole, calculated from a geometrical mean on the estimated black hole mass distribution and directly associated to the ratio of the total volume boundary of the space-time manifold and the dominant term in its Euler characteristic. The constant's small estimated value compared to the Planck scale is therefore natural and our evaluation fits remarkably well with the observed value.

gr-qc↗

arXiv2019

A topological origin for Dark Energy

Cosmology struggles with the theoretical problems generated by the observed value and recent emergence of a cosmological constant, in the standard model of cosmology, i.e. the concordance model. We propose to provide a more natural explanation for its value than the conventional quantum vacuum energy in the guise of topological invariants. Introducing topological classes densities as Lagrange multipliers, an effective cosmological constant is generated. General Relativity is reestablished by cancelling the torsion thus generated, which provides constraints on the invariants and yield the form of the effective cosmological constant. As it is divided by the total volume of spacetime, its small value compared to the Planck scale is therefore natural. It also provides a direct measurement of the global Euler number.

gr-qc↗

arXiv2017

Topological Order from a Cohomological and Higher Gauge Theory perspective

In recent years, attempts to generalize lattice gauge theories to model topological order have been carried out through the so called $2$-gauge theories. These have opened the door to interesting new models and new topological phases which are not described by previous schemes of classification. In this paper we show that we can go beyond the $2$-gauge construction when considering chain complexes of abelian groups. Based on elements of homological algebra we are able to greatly simplify already known constructions for abelian theories under a single all encompassing framework. Furthermore, this formalism allows us to systematize the computation of the corresponding topological degeneracies of the ground states and establishes a connection between them and a known cohomology, which conveniently characterizes them with a suitable set of quantum numbers.

math-ph↗

arXiv2017

Crystals from 5-vertex ice models

Given a partition $λ$ corresponding to a dominant integral weight of $\mathfrak{sl}_n$, we define the structure of crystal on the set of 5-vertex ice models satisfying certain boundary conditions associated to $λ$. We then show that the resulting crystal is isomorphic to that of the irreducible representation of highest weight $λ$.

math.RT↗

arXiv2016

Some cosmological models coming from gravitational theories having torsional degrees of freedom

In this work we consider gravitational theories in which the effect of coupling characteristic classes, appropriately introduced as operators in the Einstein-Hilbert action, has been taken into account. As it is well known, this approach strays from the framework of general relativity since it results in theories in which torsion can be present. We consider here all the characteristic classes that are consistent with a four-dimensional space-time manifold. Then, we present explicit expressions for the contortion $1$-form and torsion $2$-form that can be obtained under general conditions in various cases of interest. Additionally, we use the same framework to study cosmological scenarios that are obtained mainly by selecting the flat FLRW metric and an ideal fluid.

gr-qc↗