arXiv subjects

Ehsan Hatefi

Publications and source records attributed to Ehsan Hatefi.

At least 19 recordsLinked to original sources

arXiv2026

Stochastic analysis of finite-temperature effects on cosmological parameters by artificial neural networks

We explore the impact of finite-temperature quantum gravity effects on cosmological parameters, particularly the cosmological constant $Λ$, by incorporating temperature-dependent quantum corrections into the Hubble parameter. For that purpose, we modify the Cosmic Linear Anisotropy Solving System. We introduce new density parameters, $Ω_{Λ_2}$ and $Ω_{Λ_3}$, arising from finite-temperature quantum gravity contributions, and analyze their influence on the cosmic microwave background power spectrum using advanced machine learning techniques, including artificial neural networks and stochastic optimization. Our results reveal that $Ω_{Λ_2}$ assumes a negative value, consistent with dimensional regularization in renormalization and that the presence of $Ω_{Λ_2}$ as well as $Ω_{Λ_3}$ enhances model accuracy. Numerical analyses demonstrate that the inclusion of these parameters improves the fit to 2018 Planck data. Although further work is required, our results suggest that finite-temperature quantum gravity effects may play a non-negligible role in cosmological evolution. Although the Hubble tension persists, our findings highlight the potential of quantum gravitational corrections in refining cosmological models and motivate further investigation into higher-order thermal effects and polarization data constraints.

astro-ph.CO↗

arXiv2024

Neural Networks Assisted Metropolis-Hastings for Bayesian Estimation of Critical Exponent on Elliptic Black Hole Solution in 4D Using Quantum Perturbation Theory

It is well-known that the critical gravitational collapse produces continuous self-similar solutions characterized by the Choptuik critical exponent, $γ$. We examine the solutions in the domains of the linear perturbation equations, considering the numerical measurement errors. Specifically, we study quantum perturbation theory for the four-dimensional Einstein-axion-dilaton system of the elliptic class of $\text{SL}(2,\mathbb{R})$ transformations. We develop a novel artificial neural network-assisted Metropolis-Hastings algorithm based on quantum perturbation theory to find the distribution of the critical exponent in a Bayesian framework. Unlike existing methods, this new probabilistic approach identifies the available deterministic solution and explores the range of physically distinguishable critical exponents that may arise due to numerical measurement errors.

hep-th↗

arXiv2023

Sequential Monte Carlo with Cross-validated Neural Networks for Complexity of Hyperbolic Black Hole Solutions in 4D

This paper investigates the self-similar solutions of the Einstein-axion-dilaton configuration from type IIB string theory and the global SL(2,R) symmetry. We consider the Continuous Self Similarity (CSS), where the scale transformation is controlled by an SL(2, R) boost or hyperbolic translation. The solutions stay invariant under the combination of space-time dilation with internal SL(2,R) transformations. We develop a new formalism based on Sequential Monte Carlo (SMC) and artificial neural networks (NNs) to estimate the self-similar solutions to the equations of motion in the hyperbolic class in four dimensions. Due to the complex and highly nonlinear patterns, researchers typically have to use various constraints and numerical approximation methods to estimate the equations of motion; thus, they have to overlook the measurement errors in parameter estimation. Through a Bayesian framework, we incorporate measurement errors into our models to find the solutions to the hyperbolic equations of motion. It is well known that the hyperbolic class suffers from multiple solutions where the critical collapse functions have overlap domains for these solutions. To deal with this complexity, for the first time in literature on the axion-dilaton system, we propose the SMC approach to obtain the multi-modal posterior distributions. Through a probabilistic perspective, we confirm the deterministic $α$ and $β$ solutions available in the literature and determine all possible solutions that may occur due to measurement errors. We finally proposed the penalized Leave-One-Out Cross-validation (LOOCV) to combine the Bayesian NN-based estimates optimally. The approach enables us to determine the optimum weights while dealing with the co-linearity issue in the NN-based estimates and better predict the critical functions corresponding to multiple solutions of the equations of motion.

hep-th↗

arXiv2023

Modeling the complexity of Elliptic Black Hole Solution In 4D Using Hamiltonian Monte Carlo with Stacked Neural Networks

In this paper, we study the black hole solution of self-similar gravitational collapse in the Einstein-axion-dilaton system for the elliptic class in four dimensions. The solution is invariant under space-time dilation, which is combined with internal SL(2,R) transformations. Due to the complex and highly nonlinear pattern of the equations of motion in the physics of black holes, researchers typically have to use various numerical techniques to make the equations tractable to estimate the parameters and the critical solutions. To this end, they have to ignore the numerical measurement errors in estimating the parameters. To our knowledge, for the first time in the literature on axion-dilation systems, we propose to estimate the critical collapse functions in a Bayesian framework. We develop a novel methodology to translate the modelling of the complexity of the elliptic black hole to a sampling problem using Hamiltonian Monte Carlo with stacked neural networks. Unlike methods in the literature, this probabilistic approach enables us not only to recover the available deterministic solution but also to explore possibly all physically distinguishable self-similar solutions that may occur due to numerical measurement errors.

gr-qc↗

arXiv2023

Analysis of Black Hole Solutions in Parabolic Class Using Neural Networks

In this paper, we introduce a numerical method based on Artificial Neural Networks (ANNs) for the analysis of black hole solutions to the Einstein-axion-dilaton system in a high dimensional parabolic class. Leveraging a profile root-finding technique based on General Relativity we describe an ANN solver to directly tackle the system of ordinary differential equations. Through our extensive numerical analysis, we demonstrate, for the first time, that there is no self-similar critical solution for the parabolic class in the high dimensions of space-time. Specifically, we develop $95\%$ ANN-based confidence intervals for all the solutions in their domains. At the $95\%$ confidence level, our ANN estimators confirm that there is no black hole solution in higher dimensions, hence the gravitational collapse does not occur. Results provide some doubts about the universality of the Choptuik phenomena. Therefore, we conclude that the fastest-growing mode of the perturbations that determine the critical exponent does not exist for the parabolic class in the high dimensions.

gr-qc↗

arXiv2022

Estimation of Critical Collapse Solutions to Black Holes with Nonlinear Statistical Models

The self-similar gravitational collapse solutions to the Einstein-axion-dilaton system have already been found out. Those solutions become invariants after combining the spacetime dilation with the transformations of internal SL(2, R). We apply nonlinear statistical models to estimate the functions that appear in the physics of Black Holes of the axion-dilaton system in four dimensions. These statistical models include parametric polynomial regression, nonparametric kernel regression and semi-parametric local polynomial regression models. Through various numerical studies, we reached accurate numerical and closed-form continuously differentiable estimates for the functions appearing in the metric and equations of motion.

gr-qc↗

arXiv2022

Nonlinear Statistical Spline Smoothers for Critical Spherical Black Hole Solutions in 4-dimension

This paper focuses on self-similar gravitational collapse solutions of the Einstein--axion-dilaton configuration for two conjugacy classes of SL(2, R) transformations. These solutions are invariant under spacetime dilation, combined with internal transformations. For the first time in Einstein--axion-dilaton literature, we apply the nonlinear statistical spline regression methods to estimate the critical spherical black hole solutions in four dimension. These spline methods include truncated power basis, natural cubic spline and penalized B-spline. The prediction errors of the statistical models, on average, are almost less than $10^{-2}$, so all the developed models can be considered unbiased estimators for the critical collapse functions over their entire domains. In addition to this excellence, we derived closed forms and continuously differentiable estimators for all the critical collapse functions.

gr-qc↗

arXiv2022

On self-similar axion-dilaton configurations

We explore self-similar collapse solutions to the Einstein-axion-dilaton system in arbitrary spacetime dimensions, which are invariant under spacetime dilation combined with internal $SL(2,R)$ transformations. We set up a numerical formalism, and test it in four and five dimensions, discovering several new families of solutions in the three conjugacy classes of $SL(2,R)$.

hep-th↗

arXiv2022

On Critical Exponents for Self-Similar Collapse

We explore systematically perturbations of self-similar solutions to the Einstein-axion-dilaton system, whose dynamics are invariant under spacetime dilations combined with internal $SL(2,R)$ transformations. The self-similar solutions capture the enticing behavior critical systems on the verge of gravitational collapse, in arbitrary spacetime dimensions. Our methods rest on a combination of analytical and numerical tools, apply to all three conjugacy classes of $SL(2,R)$ transformations and allow accurate estimates of the corresponding Choptuik exponents. It is well known that these exponents depend on the spacetime dimension and on the matter content. Our main result is that they also attain different values, even within a given conjugacy class, for the distinct types of critical solutions that we recently identified in the Einstein-axion-dilaton system.

hep-th↗

arXiv2022

On Higher Dimensional Self-Similar Axion-Dilaton Solutions

We show that solutions of the self-similar gravitational collapse in the Einstein-axion-dilaton system exist in higher dimensional spacetimes. These solutions are invariant under spacetime dilation combined with internal SL(2,R) transformations. We rely on the recent setup and use it for the three different conjugacy classes (elliptic, parabolic and hyperbolic) in higher dimensions. Lastly, we identify new families of physically distinguishable self-similar solutions for all three conjugacy classes in six and seven dimensions.

hep-th↗

arXiv2022

On Perturbation Theory and Critical Exponents for Self-Similar Systems

Gravitational critical collapse in the Einstein-axion-dilaton system is known to lead to continuous self-similar solutions characterized by the Choptuik critical exponent $γ$. We complete the existing literature on the subject by computing the linear perturbation equations in the case where the axion-dilaton system assumes a parabolic form. Next, we solve the perturbation equations in a newly discovered self-similar solution in the hyperbolic case, which allows us to extract the Choptuik exponent. Our main result is that this exponent depends not only on the dimensions of spacetime but also the particular ansatz and the critical solutions that one started with.

hep-th↗

arXiv2022

On BPS World Volume, RR Couplings and their $α'$ Corrections in type IIB

We compute the asymmetric and symmetric correlation functions of a four point amplitude of a gauge field, a scalar field and a closed string Ramond-Ramond (RR) for different non-vanishing BPS branes. All world volume, Taylor and pull-back couplings and their all order $α'$ corrections have also been explored. Due to various symmetry structures, different restricted BPS Bianchi identities have also been constructed. The prescription of exploring all the corrections of two closed string RR couplings in type IIB is given. We obtain the closed form of the entire S-matrix elements of two closed string RR and a gauge field on the world volume of BPS branes in type IIB. All the correlation functions of $< V_{A^{0}(x_1)}V_{C^{-1}(z_1,\bar{z}_1)}V_{C^{-1}(z_2,\bar{z}_2)}>$ are also revealed accordingly. The algebraic forms for the most general case of the integrations $\int d^2z |z-i|^{a} |z+i|^{b} (z - \bar{z})^{c} (z + \bar{z})^{d}$ on upper half plane are derived in terms of Pochhammer and some analytic functions. Lastly, we generate various singularity structures in both effective field theory and IIB string theory, producing different contact interactions as well as their $α'$ higher derivative corrections.

hep-th↗

arXiv2021

All-Order Quartic Couplings in Highly Symmetric D-brane-Anti-D-brane Systems

We compute six-point string amplitudes for the scattering of one closed string Ramond-Ramond state, two tachyons, and two gauge fields in the worldvolume of D-brane-anti-D-brane systems in the Type II superstring theories. From the resulting S-matrix elements, we read off the precise form of the couplings, including their exact numerical coefficients, of two tachyons and two gauge fields in the corresponding highly symmetric effective field theory (EFT) Lagrangian in the worldvolume of D-brane-Anti-D-brane to all orders in $α'$, which modify and complete previous proposals. We verify that the EFT reproduces the infinite collection of stringy gauge field singularities in dual channels. Inspired by interesting similarities between the all-order highly symmetric EFTs and holographic duals of Vasiliev's higher spin gravities à là Nilsson and Vasiliev, we make a proposal for tensionless limits of D-brane-anti-D-brane systems.

hep-th↗

arXiv2019

On All-Order Higher-Point $\text{D}p$-$\overline{\text{D}p}$ Effective Actions

In this paper we derive a class of contributions to all orders in $α'$ to the effective action of D-brane-anti D-brane systems in Type II String Theory, considering an amplitude involving a closed-string Ramond-Ramond state and four open-string states: two tachyons, a scalar and a gauge boson. This type of amplitude arises in both Type IIA and Type IIB strings, and reveals a number of new effective couplings. Furthermore, we derive a series representation for the result that goes beyond a factorized limit that was recently studied, and which is expected to apply to more general six-point amplitudes of superstrings, including external fermions.

hep-th↗

arXiv2019

All Order $α'$ Corrections to Fermionic Couplings of D-brane-Anti-D-brane Effective Actions

We first point out to all order $α'$ corrections to lower order fermionic couplings and their effective actions of type II super string theory. In order to reveal all symmetries of the particular D-brane Anti-D-brane system, and to construct not only all the singularity structures but also all order $α'$ corrections of fermionic couplings to tachyons, we employ all the Conformal Field Theory (CFT) methods to a six point function. Basically, we construct all the correlation functions of four spin operators and two world sheet fermion fields. The S-matrix of two fermion fields, two real tachyons in the presence of a closed string Ramond-Ramond (RR) field in type II will be explored. Applying all the symmetries of the amplitude, a proper expansion for D-brane Anti D-brane is also found out. Having carried out all the Effective Field Theory (EFT) techniques, one would discover all order singularity structures of string theory. The entire algebraic computations of the amplitude of $ $ have also been derived. Various new string couplings are revealed as well. Eventually, making comparison the S-matrix with all EFT parts, all order $α'$ higher derivative corrections to two fermions -- two tachyons in the world volume of D-brane Anti D-brane of type II are discovered accordingly.

hep-th↗

arXiv2019

On Special Limit of Non-Supersymmetric Effective Actions of type II String theory

In this paper we first address four point functions of string amplitudes in both type IIA and IIB string theories. Making use of non-BPS scattering amplitudes, we explore not only several Bianchi identities that hold in both transverse and world volume directions of brane, but also reveal various new couplings. These couplings can just be found by taking into account the mixed pull-back and Taylor couplings where their all order alpha-prime higher derivative corrections have been derived as well. For the first time, we also explore the complete form of a six point non-BPS amplitude, involving three open string tachyons, a scalar field and a Ramond-Ramond closed string in both IIA, IIB. In a special limit of the amplitude and using the proper expansion we obtain an infinite number of bulk singularities that are being constructed in the effective field theory. Finally using new couplings we construct all the other massless and tachyon singularities in type IIA, IIB string theories. All higher derivative corrections to these new couplings to all orders in $α'$ and new restricted Bianchi identities have also been gained.

hep-th↗

arXiv2018

On Non-BPS Effective Actions of String Theory

We discuss some physical prospective of the non-BPS effective actions of type IIA and IIB superstring theories. By dealing with the complete all three and four point functions, including a closed string Ramond-Ramond (in terms of both its field strength and its potential), gauge (scalar) fields as well as a real tachyon and under symmetry structures, we find various restricted world volume and bulk Bianchi identities. The complete forms of the non-BPS scattering amplitudes including their Chan-Paton factors are elaborated. All the singularity structures of the non-BPS amplitudes, their all orders $α'$ higher derivative corrections, their contact terms and various modified Bianchi identities are derived. Finally we show that scattering amplitudes computed in different super-ghost pictures are compatible when suitable Bianchi identities are imposed on the Ramond-Ramond fields. Moreover, we argue that the higher derivative expansion in powers of the momenta of the tachyon is universal.

hep-th↗

arXiv2018

On SYM theory and all order Bulk Singularity Structures of BPS Strings in type II theory

The complete forms of the S-matrix elements of a transverse scalar field, two world volume gauge fields, and a Potential $C_{n-1}$ Ramond-Ramond (RR) form field are investigated. In order to find an infinite number of $t,s, (t+s+u)$-channel bulk singularity structures of this particular mixed open-closed amplitude, we employ all the conformal field theory techniques to $ $, exploring all the entire correlation functions and all order $α'$ contact interactions to these supersymmetric Yang-Mills (SYM) couplings. Singularity and contact term comparisons with the other symmetric analysis, $ $ and $ $ are also carried out in detail. Various couplings from pull-Back of branes, Myers terms and several generalized Bianchi identities should be taken into account to be able to reconstruct all order $α'$ bulk singularities of type IIB (IIA) superstring theory. Finally, we make a comment on how to derive without any ambiguity all order $α'$ contact terms of this S-matrix which carry momentum of RR in transverse directions.

hep-th↗