Title:	Machine learning CY metrics
DNr:	NAISS 2024/22-1601
Project Type:	NAISS Small Compute
Principal Investigator:	Magdalena Larfors <magdalena.larfors@physics.uu.se>
Affiliation:	Uppsala universitet
Duration:	2025-01-01 – 2026-01-01
Classification:	10301
Keywords:

Abstract

String theory is the leading candidate for a unification of gravity with particle physics. Unfortunately, it comes with some caveats, the main one being that it requires, between six and eight, additional dimension to be mathematically consistent. Now, in order to connect the higher dimensional theories with four dimensional observable physics one has to compactify the additional dimensions, by curling them up. The geometry of the compact manifold and a specified vector bundle over it, will in turn determine the low energy physics. The largest class of 'realistic' standard models has been obtained by compactifying on Calabi Yau manifold with vector bundles build from line bundles. The metric of these manifolds play a crucial role in the analysis. While many of its properties are known, no analytic expression for the metric has been found. This has led to a number of different numerical approximation schemes being developed. In this project we will explore and extend a TensorFlow package called cymetric, which provides a machine learning model that predicts Calabi Yau metrics. We will perform hyper parameter optimisation and other systematic studies of the architecture of the ML models. The aim is to improve accuracy and performance so that the cymetric package can be used in phenomenological string theoretic research. In the continuation of the project we will broaden the study to other ML packages for Calabi Yau metrics, and connect hyperparameter studies to recent mathematical results on the expressivity of linear, polynomial and convolutional networks by Kohn and collaborators.