Excited String States and D-branes from Infinite Width Neural Networks

TL;DR

This paper models string worldsheet path integrals using wide neural networks, extending the approach to include excited states, boundaries, and D-branes, and derives key scattering amplitudes consistent with string theory.

Contribution

It introduces a neural network framework for string worldsheet integrals that incorporates excited states and D-branes, providing explicit amplitude calculations.

Findings

Derived sphere four-point integrand with excited states

Computed disk four-tachyon amplitude on a D-brane

Recovered expected string theory factors and limits

Abstract

We explore recent proposal to represent worldsheet string path integrals by integrating over parameters of a wide random-feature neural network whose output is identified with the embedding field $X^\mu$. In this paper we extend it focusing on scattering with excited states insertions and for worldsheets with boundaries introducing fixed-feature Gaussian normal-ordering prescription for derivative composites (removing the neural contact term at finite width), and propose realization of mixed Neumann/Dirichlet boundary conditions interpreted as a neural D$p$-brane. As concrete outputs, we derive the sphere four-point integrand with a single $(1,1)$ insertion and the disk four-tachyon amplitude on a D$p$-brane, recovering the expected derivative prefactors, boundary exponents, and momentum-conservation limits after renormalization.