Nonlocal instantons and solitons in string models

TL;DR

This paper investigates nonlocal string models using local scalar fields in an auxiliary dimension, constructing solutions like instantons and solitons, and exploring their relations across different string theories.

Contribution

It introduces a novel approach to analyze nonlocal string systems via a local scalar field framework and constructs explicit solutions such as branes and instantons.

Findings

Euclidean p-adic lump as a solitonic brane

Euclidean kink as an instanton in supersymmetric string theory

Relations between solutions across different string models

Abstract

We study a class of nonlocal systems which can be described by a local scalar field diffusing in an auxiliary radial dimension. As examples p-adic, open and boundary string field theory are considered on Minkowski, Friedmann-Robertson-Walker and Euclidean metric backgrounds. Starting from distribution-like initial field configurations which are constant almost everywhere, we construct exact and approximate nonlocal solutions. The Euclidean p-adic lump is interpreted as a solitonic brane, and the Euclidean kink of supersymmetric open string field theory as an instanton. Some relations between solutions of different string theories are highlighted also thanks to a reformulation of nonlocal systems as fixed points in a renormalization group flow.