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  $$\alpha $$  <math> <mi>α</mi> </math>   and  $$\beta $$  <math> <mi>β</mi> </math>   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.

Canada

Armin Hatefi

Spain

Ehsan Hatefi

Sequential Monte Carlo with cross-validated neural networks for complexity of hyperbolic black hole solutions in 4D

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.

Roberto López-Sastre

Modeling the complexity of elliptic black hole solution in 4D using Hamiltonian Monte Carlo with stacked 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.

Analysis of black hole solutions in parabolic class using neural networks

A Correction to this paper has been published: 10.1140/epjc/s10052-020-08526-2

Italy

Eleonora Vanzan

Erratum to: On higher dimensional self-similar axion–dilaton solutions

Riccardo Antonelli

Erratum to: On critical exponents for self-similar collapse

Erratum to: On self-similar axion-dilaton configurations

Adrien Kuntz

Erratum to: On perturbation theory and critical exponents for self-similar systems

Chile

Per Sundell

Erratum to: 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 eheory (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.

China

All-order quartic couplings in highly symmetric D-brane-anti-D-brane 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  $$\gamma $$  <math> <mi>γ</mi> </math>  . 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.