arXiv subjects

Challenger Mishra

Publications and source records attributed to Challenger Mishra.

30 records · Page 2Linked to original sources

arXiv2021

Neural Network Approximations for Calabi-Yau Metrics

Ricci flat metrics for Calabi-Yau threefolds are not known analytically. In this work, we employ techniques from machine learning to deduce numerical flat metrics for the Fermat quintic, for the Dwork quintic, and for the Tian-Yau manifold. This investigation employs a single neural network architecture that is capable of approximating Ricci flat Kaehler metrics for several Calabi-Yau manifolds of dimensions two and three. We show that measures that assess the Ricci flatness of the geometry decrease after training by three orders of magnitude. This is corroborated on the validation set, where the improvement is more modest. Finally, we demonstrate that discrete symmetries of manifolds can be learned in the process of learning the metric.

hep-th↗

arXiv2020

Baryons from Mesons: A Machine Learning Perspective

Quantum chromodynamics (QCD) is the theory of the strong interaction. The fundamental particles of QCD, quarks and gluons, carry colour charge and form colourless bound states at low energies. The hadronic bound states of primary interest to us are the mesons and the baryons. From knowledge of the meson spectrum, we use neural networks and Gaussian processes to predict the masses of baryons with 90.3% and 96.6% accuracy, respectively. These results compare favourably to the constituent quark model. We as well predict the masses of pentaquarks and other exotic hadrons.

hep-ph↗

arXiv2019

Getting CICY High

Supervised machine learning can be used to predict properties of string geometries with previously unknown features. Using the complete intersection Calabi-Yau (CICY) threefold dataset as a theoretical laboratory for this investigation, we use low $h^{1,1}$ geometries for training and validate on geometries with large $h^{1,1}$. Neural networks and Support Vector Machines successfully predict trends in the number of Kähler parameters of CICY threefolds. The numerical accuracy of machine learning improves upon seeding the training set with a small number of samples at higher $h^{1,1}$.

hep-th↗

arXiv2018

Machine Learning CICY Threefolds

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbers and report a remarkable improvement over previous efforts, (2) query for favourability, and (3) predict discrete symmetries, a highly imbalanced problem to which both Synthetic Minority Oversampling Technique (SMOTE) and permutations of the CICY matrix are used to decrease the class imbalance and improve performance. In each case study, we employ a genetic algorithm to optimise the hyperparameters of the neural network. We demonstrate that our approach provides quick diagnostic tools capable of shortlisting quasi-realistic string models based on compactification over smooth CICYs and further supports the paradigm that classes of problems in algebraic geometry can be machine learned.

hep-th↗

arXiv2018

Calabi-Yau Threefolds With Small Hodge Numbers

We present a list of Calabi-Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, with small Hodge numbers, which we understand to be those manifolds with height $(h^{1,1}+h^{2,1})\le 24$. With the completion of a project to compute the Hodge numbers of free quotients of complete intersection Calabi-Yau threefolds, most of which were computed in Refs. [1-3] and the remainder in Ref. [4], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in Refs. [1, 5]. In view of this and other recent constructions of Calabi-Yau threefolds with small height, we have produced an updated list.

hep-th↗

arXiv2018

Chemical Oscillation in Ultracold Chemistry

We demonstrate the occurrence of oscillatory reactions in the ultra-cold chemistry of atom-molecular Bose-Einstein condensate. Nonlinear oscillations in the mean-field dynamics occur for a specific range of elliptic modulus, giving rise to both in- and out-phase modulations in the atom-molecule population density. The reaction front velocity is found to be controlled by photoassociation, which also regulates the condensate density. Two distinct pair of in-phase bright localized gap solitons are found as exact solutions, existence of one of which necessarily requires a background. Cnoidal atomic density-waves in a plane wave molecular background are observed in both attractive and repulsive domains. Role of intra- and inter-species interactions on both existence and stability is explicated in the presence of photoassociation.

nlin.PS↗

arXiv2017

Discrete Symmetries of Complete Intersection Calabi-Yau Manifolds

In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi- Yau manifolds and their quotients by freely-acting symmetries. These non-freely acting symmetries can appear as symmetries of low-energy theories resulting from string compactifications on these Calabi-Yau manifolds, particularly in the context of the heterotic string. Hence, our results are relevant for four-dimensional model building with discrete symmetries and they give an indication which symmetries of this kind can be expected from string theory. For the 1695 known quotients of complete intersection manifolds by freely-acting discrete symmetries, non-freely-acting, generic symmetries arise in 381 cases and are, therefore, a relatively common feature of these manifolds. We find that 9 different discrete groups appear, ranging in group order from 2 to 18, and that both regular symmetries and R-symmetries are possible.

hep-th↗

arXiv2017

Highly Symmetric Quintic Quotients

The quintic family must be the most studied family of Calabi-Yau threefolds. Particularly symmetric members of this family are known to admit quotients by freely acting symmetries isomorphic to $\mathbb{Z}_5 \times \mathbb{Z}_5$. The corresponding quotient manifolds may themselves be symmetric. That is, they may admit symmetries that descend from the symmetries that the manifold enjoys before the quotient is taken. The formalism for identifying these symmetries was given a long time ago by Witten and instances of these symmetric quotients were given also, for the family $\mathbb{P}^7[2, 2, 2, 2]$, by Goodman and Witten. We rework this calculation here, with the benefit of computer assistance, and provide a complete classification. Our motivation is largely to develop methods that apply also to the analysis of quotients of other CICY manifolds, whose symmetries have been classified recently. For the $\mathbb{Z}_5 \times \mathbb{Z}_5$ quotients of the quintic family, our list contains families of smooth manifolds with symmetry $\mathbb{Z}_4$, $\text{Dic}_3$ and $\text{Dic}_5$, families of singular manifolds with four conifold points, with symmetry $\mathbb{Z}_6$ and $\mathbb{Q}_8$, and rigid manifolds, each with at least a curve of singularities, and symmetry $\mathbb{Z}_{10}$. We intend to return to the computation of the symmetries of the quotients of other CICYs elsewhere.

hep-th↗

arXiv2015

Hodge Numbers for CICYs with Symmetries of Order Divisible by 4

We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kähler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, $G$, that arise in the classification are either $Z_2$ or contain $Z_4$, $Z_2 \times Z_2$, $Z_3$ or $Z_5$ as a subgroup. The Hodge numbers for the quotients for which the group $G$ contains $Z_3$ or $Z_5$ have been computed previously. This paper deals with the remaining cases, for which $G \supseteq Z_4$ or $G\supseteq Z_2 \times Z_2$. We also compute the Hodge numbers for 99 of the 166 CICY's which have $Z_2$ quotients.

hep-th↗

arXiv2015

The Family Problem: Hints from Heterotic Line Bundle Models

Within the class of heterotic line bundle models, we argue that N=1 vacua which lead to a small number of low-energy chiral families are preferred. By imposing an upper limit on the volume of the internal manifold, as required in order to obtain finite values of the four-dimensional gauge couplings, and validity of the supergravity approximation we show that, for a given manifold, only a finite number of line bundle sums are consistent with supersymmetry. By explicitly scanning over this finite set of line bundle models on certain manifolds we show that, for a sufficiently small volume of the internal manifold, the family number distribution peaks at small values, consistent with three chiral families. The relation between the maximal number of families and the gauge coupling is discussed, which hints towards a possible explanation of the family problem.

hep-th↗

arXiv2011

New cross-phase modulated localized solitons in coupled atomic-molecular BEC

The interacting atom-molecule BEC (AMBEC) dynamics is investigated in the mean field ap- proach. The presence of atom-atom, atom-molecule and molecule-molecule interactions, coupled with a characteristically different interaction representing atom-molecule interconversion, endows this system with nonlinearities, which differ significantly from the standard Gross-Pitaevskii (GP) equation. Exact localized solutions are found to belong to two distinct classes. The first ones are analogous to the soliton solutions of the weakly coupled GP equation, whereas the second non- equivalent class is related to the solitons of the strongly coupled BEC. Distinct parameter domains characterize these solitons, some of which are analogous to the complex profile Bloch solitons in magnetic systems. These localized solutions are found to represent a variety of phenomena, which include co-existence of both atom-molecule complex and miscible-immiscible phases. Numerical sta- bility is explicitly checked, as also the stability analysis based on the study of quantum uctuations around our solutions. We also find out the domain of modulation instability in this system.

cond-mat.quant-gas↗

arXiv2011

Grey solitons in doped nonlinear fibers

Grey solitons, with complex envelope, are obtained as exact solutions of the coupled system describing doped optical nonlinear fibers. The phase degree of freedom plays a crucial role in removing the restrictive equal frequency conditions on the tanh-sech paired pulses, identified earlier [1]. The cross-phase modulation is found to control the speed of the grey soliton, which has an upper bound. The coupled soliton solution obtained here was found to be stable in a wide parameter range.

quant-ph↗