arXiv subjects

Nana Cabo Bizet

Publications and source records attributed to Nana Cabo Bizet.

16 recordsLinked to original sources

arXiv2025

Energy-time uncertainty relation from entropy measures

In a previous study, it was shown that the Generalized Uncertainty Principle (GUP) can be derived from non-extensive entropies, particularly those depending only on the probability, denoted as $S_\pm$ in the literature. This finding reveals an intriguing connection between non-extensive statistics and quantum gravity. In the present work, we extend our previous result and derive a generalized energy-time uncertainty relation based on a measure of non-extensive entropies. Consequently, the dispersion relation undergoes modifications consistent with those obtained in other approaches to quantum gravity. We interpret these modifications as evidence of the non-extensive behavior of spacetime fluctuations at scales close to the Planck scale. While these effects are significant in this regime, they become negligible in the classical one, i.e. at low energies where the spacetime is smooth. As a consequence of the non-extensive behavior exhibited by spacetime at very small scales, the black hole radiation temperature undergoes quantum-level corrections, increasing in the case of $ S_{-} $ and decreasing for the case of $ S_{+} $. Moreover, the modified uncertainty relation derived here predicts a maximum uncertainty in energy, of the order of Planck energy, and a minimum time interval, of the order of the Planck time, offering new insights into the fundamental structure of spacetime in the quantum regime.

hep-th↗

arXiv2024

Scale hierarchies near the conifold

We study the axio-dilaton and complex structure stabilization for a generic one-parameter Calabi-Yau (CY) compactification. We focus on near the conifold regions and consider a strongly warped metric. We analyze numerically the case of the mirror of the quintic CY. The axio-dilaton $τ$ and complex structure $z$ moduli are stabilized simultaneously comparing with previous results, showing that generically $z$ is heavier than $τ$, and the axio-dilaton can not be fixed first. This is also the case when we add the warping correction to the potential; and in general this inclusion does not destabilize the moduli. We point out why in this setup non-supersymmetric vacua are much more dense than supersymmetric vacua. We study the dependence of the vacua stabilization by addition of an $\overline{D3}$-brane, for a fixed volume. The vacuum state masses have divergent eigenvalues near the conifold singularity that gets softened by the warping correction. Generically the considered contributions allow to find stable vacua in this setup. The scale hierarchy between 6D and 4D; arising from the warping, as stated by Giddings Kachru and Polchinski (GKP), is preserved; while the masses in the vacua acquire physically reasonable values.

hep-th↗

arXiv2024

T-dualities in gauged linear sigma models

We describe non-Abelian T-dualities for $\mathcal{N} = 2$ two dimensional gauged linear sigma model (GLSM). We start with the case of left and right $(2, 2)$ supersymmetry (SUSY), $U(1)$ gauge group, and global non-Abelian symmetries. Our analysis applies to the specialization of the GLSM with the global group $SU(2)\times SU(2)$, whose original model is the resolved conifold. We analyze the dual model and compute the periods on the dual geometry, matching the effective potential for the $U(1)$ gauge field, and discuss the coincident singularity at the conifold point. We further present the non-Abelian T-dualization of models with $(0,2)$ SUSY, analyzing the case of global symmetry $SU(2)$. In this case the full non-Abelian duality can be solved. The dual geometries with and without non-perturbative corrections to the superpotential coincide. The structure of the dual non-perturbative corrections employed are determined based on symmetry arguments. The non-Abelian T-dualities reviewed here lead to potential new symmetries between physical theories.

hep-th↗

arXiv2022

Modified entropies as the origin of generalized uncertainty principles

The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with $S_{+}$ and $S_-$ entropies are negative and positive respectively. This allows us to explore various possibilities in the search of physical implications. We conclude that non-extensive statistics constitutes a signature of quantum gravity.

quant-ph↗

arXiv2022

Variations of the SIR model for COVID-19 evolution

In this work, we discuss the SIR epidemiological model and different variations of it applied to the propagation of the COVID-19 pandemia; we employ the data of the state of Guanajuato and of Mexico. We present some considerations that can improve the predictions made by those models. We consider a time-dependent infection rate, which we adjust to the data. Starting from a linear regime where the populations are much smaller that the country or state population and the population of susceptible (S) can be approximated in convenient units to S approximately 1, we make fits of the parameters. We also consider the case when the susceptible starts departing from 1, for this case we adjust an effective contagion rate. We also explore the ratio of detected populations and the real ones, obtaining that -for the analyzed case it is of approximately 10%. We estimate the number of deaths by making a fit versus the recovered cases, this fit is in first approximation linear, but other powers can give a good agreement. By predictions to past data, we conclude that adaptations of the SIR model can be of great use in describing pandemia's propagation, specially in limited time periods.

q-bio.PE↗

arXiv2020

Testing Swampland Conjectures with Machine Learning

We consider Type IIB compactifications on an isotropic torus $T^6$ threaded by geometric and non geometric fluxes. For this particular setup we apply supervised machine learning techniques, namely an artificial neural network coupled to a genetic algorithm, in order to obtain more than sixty thousand flux configurations yielding to a scalar potential with at least one critical point. We observe that both stable AdS vacua with large moduli masses and small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the Refined de Sitter Conjecture. Moreover, by considering a hierarchy among fluxes, we observe that perturbative solutions with small values for the vacuum energy and moduli masses are favored, as well as scenarios in which the lightest modulus mass is much greater than the corresponding AdS vacuum scale. Finally we apply some results on Random Matrix Theory to conclude that the most probable mass spectrum derived from this string setup is that satisfying the Refined de Sitter and AdS scale conjectures.

hep-th↗

arXiv2020

Modelos SIR modificados para la evolución del COVID19

We study the SIR epidemiological model, with a variable contagion rate, applied to the evolution of COVID19 in Cuba. It is highlighted that an increase in the predictive character depends on understanding the dynamics for the temporal evolution of the rate of contagion $β^*$. A semi-empirical model for this dynamics is formulated, where reaching $β^*\approx0$ due to isolation is achieved after the mean duration of the disease $τ=1/γ$, in which the number of infected in the confined families has decreased. It is considered that $β^*(t)$ should have an abrupt decrease on the day of initiation of confinement and decrease until canceling at the end of the interval $τ$. The analysis describes appropriately the infection curve for Germany. The model is applied to predict an infection curve for Cuba, which estimates a maximum number of infected as less than 2000 in the middle of May, depending on the rigor of the isolation. This is suggested by the ratio between the daily detected cases and the total. We consider the ratio between the observed and real infected cases (k) less than unity. The low value of k decreases the maximum obtained when $β^*-γ>0$. The observed evolution is independent of k in the linear region. The value of $β^*$ is also studied by time intervals, adjusting to the data of Cuba, Germany and South Korea. We compare the extrapolation of the evolution of Cuba with the contagion rate until 16.04.20 with that obtained by a strict quarantine at the end of April. This model with variable $β^*$ correctly describes the observed infected evolution curves. We emphasize that the desired maximum of the SIR infected curve is not the maximum standard with constant $β^*$, but one achieved due to quarantine when $\tilde R_0=β^*/γ<1$. For the countries controlling the epidemic the maxima are in the region in which SIR equations are linear.

q-bio.PE↗

arXiv2020

Generalised asymptotic equivalence for extensive and non-extensive entropies

We extend the Hanel and Thurner asymptotic analysis to both extensive and non-extensive entropies on the basis of a wide class of entropic forms. The procedure is known to be capable to classify multiple entropy measures in terms of their defining equivalence classes. Those are determined by a pair of scaling exponents taking into account a large number of microstates as for the thermodynamical limit. Yet, a generalisation to this formulation makes it possible to establish an entropic connection between Markovian and non-Markovian statistical systems through a set of fundamental entropies $S_{\pm}$, which have been studied in other contexts and exhibit, among their attributes, two interesting aspects: They behave as additive for a large number of degrees of freedom while they are substantially non-additive for a small number of them. Furthermore, an ample amount of special entropy measures, either additive or non-additive, are contained in such asymptotic classification. Under this scheme we analyse the equivalence classes of Tsallis, Sharma-Mittal and Rényi entropies and study their features in the thermodynamic limit as well as the correspondences among them.

cond-mat.stat-mech↗

arXiv2019

A toolkit for twisted chiral superfields

We calculate the most general terms for arbitrary Lagrangians of twisted chiral superfields in 2D (2,2) supersymmetric theories [1]. The scalar and fermion kinetic terms and interactions are given explicitly. We define a set of twisted superspace coordinates, which allows to obtain Lagrangian terms for generic Kähler potential and generic twisted superpotential; this is done in analogy to the corresponding chiral superfields calculations [2]. As examples we obtain the Lagrangian of a single twisted superfield, i.e. the Abelian-dual of the gauged linear sigma model (GLSM) of a single chiral superfield, and the Lagrangian for the non-Abelian SU(2) dual of the $\mathbb{CP}^1$ GLSM model. Generic Lagrangians contain both twisted-chiral and chiral superfields, with distinct representations. We write down the kinetic terms for all bosons and fermions as well as their interactions for these generic cases. As twisted superfields play a central role for T-dualities and Mirror Symmetry in GLSMs, we expect the pedagogical exposition of this techniques to be useful in those studies.

hep-th↗

arXiv2019

Leaving the Swampland: Non-geometric fluxes and the Distance Conjecture

We study a Type IIB isotropic toroidal compactification with non-geometric fluxes. Under the assumption of a hierarchy on the moduli, an effective scalar potential is constructed showing a runaway direction on the real part of the Kähler modulus while the rest of the moduli are stabilized. For the effective model to be consistent it is required that displacements in the field space are finite. Infinite distances in field space would imply a breakdown in the hierarchy assumption on the moduli. In this context, the Swampland Distance Conjecture is satisfied suggesting the possibility of leaving or entering the Swampland by a parametric control of the fluxes. This is achieved upon allowing the non-geometric fluxes to take fractional values. In the process we are able to compute the cut-off scale below which the theory is valid, completely depending on the flux configuration. We also report on the appearance of a discrete spectrum of values for the string coupling at the level of the effective theory.

hep-th↗

arXiv2019

Quantum implications of non-extensive statistics

Exploring the analogy between quantum mechanics and statistical mechanics we formulate an integrated version of the Quantropy functional [1]. With this prescription we compute the propagator associated to Boltzmann-Gibbs statistics in the semiclassical approximation as $K=F(T) \exp\left(i S_{cl}/\hbar\right)$. We determine also propagators associated to different non-additive statistics; those are the entropies depending only on the probability $S_{\pm}$ [2] and Tsallis entropy $S_q$ [3]. For $S_{\pm}$ we obtain a power series solution for the probability vs. the energy, which can be analytically continued to the complex plane, and employed to obtain the propagators. Our work is motivated by [4] where a modified q-Schrödinger equation is obtained; that provides the wave function for the free particle as a q-exponential. The modified q-propagator obtained with our method, leads to the same q-wave function for that case. The procedure presented in this work allows to calculate q-wave functions in problems with interactions; determining non-linear quantum implications of non-additive statistics. In a similar manner the corresponding generalized wave functions associated to $S_{\pm}$ can also be constructed. The corrections to the original propagator are explicitly determined in the case of a free particle and the harmonic oscillator for which the semi-classical approximation is exact.

cond-mat.stat-mech↗

arXiv2019

Non Abelian T-duality in Gauged Linear Sigma Models

Abelian T-duality in Gauged Linear Sigma Models (GLSM) forms the basis of the physical understanding of Mirror Symmetry as presented by Hori and Vafa. We consider an alternative formulation of Abelian T-duality on GLSM's as a gauging of a global $U(1)$ symmetry with the addition of appropriate Lagrange multipliers. For GLSMs with Abelian gauge groups and without superpotential we reproduce the dual models introduced by Hori and Vafa. We extend the construction to formulate non-Abelian T-duality on GLSMs with global non-Abelian symmetries. The equations of motion that lead to the dual model are obtained for a general group, they depend in general on semi-chiral superfields; for cases such as $SU(2)$ they depend on twisted chiral superfields. We solve the equations of motion for an $SU(2)$ gauged group with a choice of a particular Lie algebra direction of the vector superfield. This direction covers a non-Abelian sector that can be described by a family of Abelian dualities. The dual model Lagrangian depends on twisted chiral superfields and a twisted superpotential is generated. We explore some non-perturbative aspects by making an Ansatz for the instanton corrections in the dual theories. We verify that the effective potential for the $U(1)$ field strength in a fixed configuration on the original theory matches the one of the dual theory. Imposing restrictions on the vector superfield, more general non-Abelian dual models are obtained. We analyze the dual models via the geometry of their susy vacua.

hep-th↗

arXiv2016

Revisiting constraints on uplifts to de Sitter vacua

We revisit the issue of uplifting the potential to de Sitter (dS) vacua in type IIB flux compactifications of Kachru, Kallosh, Linde and Trivedi (KKLT). We shed light on some tension between two constraints on dS vacua in type IIB string theory. One is the well-known and much-discussed constraint which leads to the no-go theorem that can in principle be evaded. The other follows from 4-dimensional Einstein's equations, which has, however, been much less discussed in connection with the former constraint. In addition to the challenges previously posed, it is suggested that the uplifting scenarios, in particular, obstruct the evasion of the no-go theorem more strongly than one might have assumed.

hep-th↗

arXiv2016

Mirror quintic vacua: hierarchies and inflation

We study the moduli space of type IIB string theory flux compactifications on the mirror of the CY quintic 3-fold in P4. We focus on the dynamics of the four dimensional moduli space, defined by the axio-dilaton τ and the complex structure modulus z. The z-plane has critical points, the conifold, the orbifold and the large complex structure with non trivial monodromies. We find the solutions to the Picard-Fuchs equations obeyed by the periods of the CY in the full z-plane as a series expansion in z around the critical points to arbitrary order. This allows us to discard fake vacua, which appear as a result of keeping only the leading order term in the series expansions. Due to monodromies vacua are located at a given sheet in the z-plane. A dS vacuum appears for a set of fluxes. We revisit vacua with hierarchies among the 4D and 6D physical scales close to the conifold point and compare them with those found at leading order in [1, 2]. We explore slow-roll inflationary directions of the scalar potential by looking at regions where the multi-field slow-roll parameters ε and η are smaller than one. The value of ε depends strongly on the approximation of the periods and to achieve a stable value, several orders in the expansion are needed. We do not find realisations of single field axion monodromy inflation. Instead, we find that inflationary regions appear along linear combinations of the four real field directions and for certain configurations of fluxes.

hep-th↗

arXiv2015

Generalized entanglement entropy and holography

In this work, we first introduce a generalized von Neumann entropy that depends only on the density matrix. This is based on a previous proposal by one of us modifying the Shannon entropy by considering non-equilibrium systems on stationary states, and an entropy functional depending only on the probability. We propose a generalization of the replica trick and find that the resulting modified von Neumann entropy is precisely the previous mentioned entropy that was obtained by other assumptions. Then, we address the question whether alternative entanglement entropies can play a role in the gauge/gravity duality. Our focus are 2d CFT and their gravity duals. Our results show corrections to the von Neumann entropy $S_0$ that are larger than the usual $UV$ ones and also than the corrections to the length dependent $AdS_3$ entropy which result comparable to the $UV$ ones. The correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT and the gravitational $AdS_3$ entropies.

hep-th↗

arXiv2014

Landscaping with fluxes and the E8 Yukawa Point in F-theory

Integrality in the Hodge theory of Calabi-Yau fourfolds is essential to find the vacuum structure and the anomaly cancellation mechanism of four dimensional F-theory compactifications. We use the Griffiths-Frobenius geometry and homological mirror symmetry to fix the integral monodromy basis in the primitive horizontal subspace of Calabi-Yau fourfolds. The Gamma class and supersymmetric localization calculations in the 2d gauged linear sigma model on the hemisphere are used to check and extend this method. The result allows us to study the superpotential and the Weil-Petersson metric and an associated tt* structure over the full complex moduli space of compact fourfolds for the first time. We show that integral fluxes can drive the theory to N=1 supersymmetric vacua at orbifold points and argue that fluxes can be chosen that fix the complex moduli of F-theory compactifications at gauge enhancements including such with U(1) factors. Given the mechanism it is natural to start with the most generic complex structure families of elliptic Calabi-Yau 4-fold fibrations over a given base. We classify these families in toric ambient spaces and among them the ones with heterotic duals. The method also applies to the creating of matter and Yukawa structures in F-theory. We construct two SU(5) models in F-theory with a Yukawa point that have a point on the base with an $E_8$-type singularity on the fiber and explore their embeddings in the global models. The explicit resolution of the singularity introduce a higher dimensional fiber and leads to novel features.

hep-th↗