Published Papers by Math-Phys-Cat Group
Supersymmetric gauge theories have been some of the most interesting objects of study in Theoreti... more Supersymmetric gauge theories have been some of the most interesting objects of study in Theoretical Physics for the past 40 years or so. In this talk, I will focus on N=2 SYM, more specifically on Seiberg-Witten theory, which is concerned with studying its low-energy prepotential. It is known that the only corrections to the classical prepotential are non-perturbative and 1-loop perturbative. We will see how to calculate the instanton contribution for U(N) theories. In order to do so, I will show how the concept of localization is applied in Physics through the Mathai-Quillen formalism. Then, I will introduce Nekrasov’s Ω-deformation: it uses the ADHM construction and localization to compute the instanton contribution in the Ω-deformed theory. By taking the deformation to zero, we solve the problem in Seiberg-Witten theory.
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For any finite number of parts, measurements and outcomes in a Bell scenario we estimate the prob... more For any finite number of parts, measurements and outcomes in a Bell scenario we estimate the probabilityof random N-qudit pure states to substantially violate any Bell inequality with uniformly bounded coefficients.We prove that under some conditions on the local dimension the probability to find any significant amount ofviolation goes to zero exponentially fast as the number of parts goes to infinity. In addition, we also prove that ifthe number of parts is at least 3, this probability also goes to zero as the the local Hilbert space dimension goesto infinity.
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We study a finite spin-1 2 Ising chain with a spatially alternating transverse field of period 2.... more We study a finite spin-1 2 Ising chain with a spatially alternating transverse field of period 2. By means of a Jordan-Wigner transformation for even and odd sites, we are able to map it into a one-dimensional model of free fermions. We determine the ground-state energies in the positive-and negative-parity subspaces (subspaces with an even or odd total number of down spins, respectively) and compare them in order to establish the ground-state energy for the entire Hamiltonian. We derive closed-form expressions for this energy gap between the different parity subspaces and analyze its behavior and dependence on the system size in the various regimes of the applied field. Finally, we suggest an expression for the correlation length of such a model that is consistent with the various values found in the literature for its behavior in the vicinity of critical points.
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To explain aspects of the quantum-to-classical transition, quantum Darwinism explores the fact th... more To explain aspects of the quantum-to-classical transition, quantum Darwinism explores the fact that, due to interactions between a quantum open system and its surrounding environment, information about the system can be spread redundantly to the environment. Here we recall that there are in the literature two distinct and non-equivalent ways to make this statement precise and quantitative. We first point out the difference with some simple but illustrative examples. We then consider a model where Darwinism can be seen from both perspectives. Moreover, the non-Markovianity of our model can be varied with a parameter. In a recent work [F. Galve et al., Sci. Reps. 6, 19607 (2016)], the authors concluded that quantum Darwinism can be hindered by non-Markovianity. We depart from their analysis and argue that, from both perspectives to quantum Darwinism, there is no clear relationship between non-Markovianity and quantum Darwinism in our model.
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This work is devoted to the investigation of nontrivial transport properties in many-body quantum... more This work is devoted to the investigation of nontrivial transport properties in many-body quantum systems. Precisely, we study transport in the steady state of spin-1/2 Heisenberg XXZ chains, driven out of equilibrium by two magnetic baths at their end points. We take graded versions of the model, i.e., asymmetric chains in which some structure gradually changes in space. We investigate how we can manipulate and control the energy and spin currents of such chains by tuning external and/or inner parameters. In particular, we describe the occurrence of energy current rectification and its reversal due to the application of external magnetic fields. We show that, after carefully chosen inner parameters for the system, by turning on an external magnetic field we can find spin and energy currents propagating in different directions. More interestingly, we may find cases in which rectifications of energy and spin currents occur in opposite directions, i.e., if the energy current is larger when flowing from left to right side, then the spin current is larger if it flows from right to left side. We still describe situations with inversion of the energy current direction as we increase the system asymmetry. We stress that our work aims the development of theoretical knowledge as well as the stimulation of future experimental applications.
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In this work we study and compare the features of gravitational entropy near the throat of transv... more In this work we study and compare the features of gravitational entropy near the throat of transversable wormholes formed by exotic matter and wormholes in galactic halos. We have verified that gravitational entropy and entropy density of these wormholes in regions near their throats are indistinguishable for objects of same throat, despite the fact they are described by different metrics and by distinct energy-momentum tensors. We have found that the gravitational entropy density diverges near the throat for both cases, probably due to a non-trivial topology at this point, however allowing the interesting interpretation that a maximum flux of information can be carried through the throat of these wormholes. In addition, we have found that both are endowed with an entropic behaviour similar to Hawking-Bekenstein's entropy of non-rotating and null charge black holes.
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We investigate in detail the interaction between the spin-1/2 fields endowed with mass dimension ... more We investigate in detail the interaction between the spin-1/2 fields endowed with mass dimension one and the graviton. We obtain an interaction vertex that combines the characteristics of scalar-graviton and Dirac's fermion-graviton vertices, due to the scalar-dynamic attribute and the fermionic structure of this field. It is shown that the vertex obtained obeys the Ward-Takahashi identity, ensuring the gauge invariance for this interaction. In the contribution of the mass dimension one fermion to the graviton propagator at one-loop, we found the conditions for the cancellation of the tadpole term by a cosmological counter-term. We calculate the scattering process for arbitrary momentum. For low energies, the result reveals that only the scalar sector present in the vertex contributes to the gravitational potential. Finally, we evaluate the non relativistic limit of the gravitational interaction and obtain an attractive Newtonian potential, as required for a dark matter candidate.
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A Friedmann like cosmological model in Einstein-Cartan framework is studied when the torsion func... more A Friedmann like cosmological model in Einstein-Cartan framework is studied when the torsion function is assumed to be proportional to a single φ(t) function coming just from the spin vector contribution of ordinary matter. By analysing four different types of torsion function written in terms of one, two and three free parameters, we found that a model with φ(t) = −αH(t) ρ m (t)/ρ 0c n is totally compatible with recent cosmological data, where α and n are free parameters to be constrained from observations, ρ m is the matter energy density and ρ 0c the critical density. The recent accelerated phase of expansion of the universe is correctly reproduced by the contribution coming from torsion function, with a deceleration parameter indicating a transition redshift of about 0.65. * Electronic address: s.pereira@unesp.br † Electronic address: rodrigo.lima@feg.unesp.br ‡ Electronic address: jf.jesus@unesp.br § Electronic address: holandarfl@fisica.ufrn.br 1 arXiv:1906.07624v2 [gr-qc]
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In this theoretical communication we look towards understand the underlying phe-nomenology concer... more In this theoretical communication we look towards understand the underlying phe-nomenology concerning the Elko spinors within VSR theory. The program to be accomplished here start when we define the eigenspinors of the charge conjugation operator as eigenstates of the helicity operator in the Cartesian coordinates system. This prescription is very useful in the sense of phenomenological point of view, so, we propose a set of Elko spinors ready to be computationally implemented. Regardless of, in order to show the application of given approach we impose to these spinors to be restrict to an axis, coincidentally the axis of locality [1, 2], and then, using the proposed prescription, we search for physical amounts and physical processes by analysing the Yukawa and the self-interaction in such framework.
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In the present article we study the process of particle creation for Elko spinor fields as a cons... more In the present article we study the process of particle creation for Elko spinor fields as a consequence of expansion of the universe. We study the effect driven by a expanding background that is asymptotically minkowskian in the past and future. The differential equation that governs the time mode function is obtained for the conformal coupling case and, although its solution is non-analytic, within an approximation that preserves the characteristics of the terms that break the analyticity, analytic solutions are obtained. Thus, by means of the Bogolyubov transformations technique, the number density of particles created is obtained, which can be compared to exact solutions already present in literature for scalar and Dirac particles. The spectrum of created particles is obtained and it was found that it is a generalization of the scalar field case, which converges to the scalar field one when the specific terms concerning the Elko field are dropped out. We also found that lighter Elko particles are created in larger quantities than Dirac fermionic particles. By considering the Elko particles as candidate to dark matter in the universe, such result shows that there are more light dark matter (Elko) particles created by gravitational effects in the universe than baryonic (fermionic) matter, in agreement to standard model.
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Vector bundles and double vector bundles, or 2-fold vector bundles, arise naturally for instance ... more Vector bundles and double vector bundles, or 2-fold vector bundles, arise naturally for instance as base spaces for algebraic structures such as Lie algebroids, Courant algebroids and double Lie algebroids. It is known that all these structures possess a unified description using the language of supergeometry and Z-graded manifolds of degree ≤ 2. Indeed, a link has been established between the super and classical pictures by the geometrization process, leading to an equivalence of the category of Z-graded manifolds of degree ≤ 2 and the category of (double) vector bundles with additional structures. In this paper we study the geometrization process in the case of Z r-graded manifolds of type ∆, where ∆ is a certain weight system and r is the rank of ∆. We establish an equivalence between a subcategory of the category of n-fold vector bundles and the category of graded manifolds of type ∆.
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Geometriae Dedicata (2016) 183(1) 25-31, 2019
Let (E, φ) be a rank two co-Higgs vector bundles on a Kähler compact surface X with φ ∈ H 0 (X, E... more Let (E, φ) be a rank two co-Higgs vector bundles on a Kähler compact surface X with φ ∈ H 0 (X, End(E) ⊗ T X) nilpotent. If (E, φ) is semi-stable, then one of the following holds up to finiteétale cover: i) X is uniruled. ii) X is a torus and (E, φ) is strictly semi-stable. iii) X is a properly elliptic surface and (E , φ) is strictly semi-stable.
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We introduce an algorithm to find possible constants of motion for a given replicator equation. T... more We introduce an algorithm to find possible constants of motion for a given replicator equation. The algorithm is inspired by Dirac geometry and a Hamiltonian description for the replicator equations with such constants of motion, up to a time re-parametrization, is provided using Dirac\big-isotropic structures. Using the equivalence between replicator and Lotka-Volterra (LV) equations, the set of conservative LV equations is enlarged. Our approach generalizes the well-known use of gauge transformations to skew-symmetrize the interaction matrix of a LV system. In the case of predator-prey model, our method does allow interaction between different predators and between different preys.
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The paper is devoted to a computation of the Lie superalgebras of holomorphic vector fields on is... more The paper is devoted to a computation of the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebras $\mathfrak{osp}_{2m|2n}(\mathbb C)$ and $\pi\mathfrak{sp}_{n}(\mathbb C)$. The result is that under some restrictions on the flag type any holomorphic vector field is fundamental with respect to the natural action of the Lie superalgebras $\mathfrak{osp}_{2m|2n}(\mathbb C)$ or $\pi\mathfrak{sp}_{n}(\mathbb C)$.
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We compute the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of... more We compute the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebra osp 2m−1|2n (C).
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We prove three obstruction results on the existence of equations of state in clusters of stellar ... more We prove three obstruction results on the existence of equations of state in clusters of stellar systems fulfilling mass-radius relations and some additional bound (on the mass, on the radius or a causal bound). The theorems are proved in great generality. We start with a motivating example of TOV systems and apply our results to stellar systems arising from experimental data.
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The Tolman-Oppenheimer-Volkoff (TOV) equations are a partially uncoupled system of nonlinear and ... more The Tolman-Oppenheimer-Volkoff (TOV) equations are a partially uncoupled system of nonlinear and non-autonomous ordinary differential equations which describe the structure of isotropic spherically symmetric static fluids. Nonlinearity makes finding explicit solutions of TOV systems very difficult and such solutions and very rare. In this paper we introduce the notion of pseudo-asymptotic TOV systems and we show that the space of such systems is at least fifteen-dimensional. We also show that if the system is defined in a suitable domain (meaning the extended real line), then well-behaved pseudo-asymptotic TOV systems are genuine TOV systems in that domain, ensuring the existence of new fourteen analytic solutions for extended TOV equations. The solutions are classified according to the nature of the matter (ordinary or exotic) and to the existence of cavities and singularities. It is shown that at least three of them are realistic, in the sense that they are formed only by ordinary matter and contain no cavities or singularities.
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Topological and Geometric Obstructions on Einstein-Hilbert-Palatini Theories, 2019
In this article we introduce A-valued Einstein-Hilbert-Palatini functional (A-EHP) over a n-manif... more In this article we introduce A-valued Einstein-Hilbert-Palatini functional (A-EHP) over a n-manifold M , where A is an arbitrary graded algebra, as a generalization of the functional arising in the study of the first order formulation of gravity. We show that if A is weak (k, s)-solvable, then A-EHP is non-null only if n < k + s + 3. We prove that essentially all algebras modeling classical geometries (except semi-Riemannian geometries with specific signatures) satisfy this condition for k = 1 and s = 2, including Hitchin’s generalized complex geometry, Pantilie’s generalized quaternionic geometries and all other generalized Cayley-Dickson geometries. We also prove that if A is concrete in some sense, then a torsionless version of A-EHP is non-null only if M is Kähler of dimension n = 2, 4. We present our results as obstructions to M being an Einstein manifold relative to geometries other than semi-Riemannian.
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Preprints by Math-Phys-Cat Group
In this paper we continue the program on the classification of extensions of the Standard Model o... more In this paper we continue the program on the classification of extensions of the Standard Model of Particle Physics started in arXiv:2007.01660. We propose four complementary questions to be considered when trying to classify any class of extensions of a fixed Yang-Mills-type theory S G : existence problem, obstruction problem, maximality problem and universality problem. We prove that all these problems admits a purely categorical characterization internal to the category of extensions of S G. Using this we show that maximality and universality are dense properties, meaning that if they are not satisfied in a class E(S G ;Ĝ), then they are in their "one-point compactification" E(S G ;Ĝ) ∪Ŝ by a specific trivial extensionŜ. We prove that, by means of assuming the Axiom of Choice, one can get another maximality theorem, now independent of the trivial extensionŜ. We consider the class of almost coherent extensions, i.e, complete, injective and of pullback-type, and we show that for it the existence and obstruction problems have a complete solution. Using again the Axiom of Choice, we prove that this class of extensions satisfies the hypothesis of the second maximality theorem.
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In this paper we consider the classification problem of extensions of Yang-Mills-type (YMT) theor... more In this paper we consider the classification problem of extensions of Yang-Mills-type (YMT) theories. For us, a YMT theory differs from the classical Yang-Mills theories by allowing an arbitrary pairing on the curvature. The space of YMT theories with a prescribed gauge group G and instanton sector P is classified, an upper bound to its rank is given and it is compared with the space of Yang-Mills theories. We present extensions of YMT theories as a simple and unified approach to many different notions of deformations and addition of correction terms previously discussed in the literature. A relation between these extensions and emergence phenomena in the sense of [34] is presented. We consider the space of all extensions of a fixed YMT theory S G and we prove that for every additive group action of G in R and every commutative and unital ring R, this space has an induced structure of R[G]-module bundle. We conjecture that this bundle can be continuously embedded into a trivial bundle. Morphisms between extensions of a fixed YMT theory are defined in such a way that they define a category of extensions. It is proved that this category is a reflective subcategory of a slice category, reflecting some properties of its limits and colimits.
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Published Papers by Math-Phys-Cat Group
Preprints by Math-Phys-Cat Group
on $C^{k}$-manifolds $M$ whose coefficients are as regular as one
needs. We show that if $M$ admits a suitable subatlas, meaning a
$\mathcal{B}_{\alpha,\beta}^{k}$-structure for a certain presheaf
of Fr\'echet spaces $B$ and for certain functions $\alpha$ and
$\beta$, then the existence of such regular connections can be established.
It is also proved that if the $\mathcal{B}_{\alpha,\beta}^{k}$-structure
is actually nice (in the sense of \citep{Bk_manifolds}), then a multiplicity
result can also be obtained by means of Thom's transversality arguments.