On the trivalent junction of three non-tachyonic heterotic string theories

TL;DR

This paper constructs a junction connecting three distinct ten-dimensional heterotic string theories using a specialized two-dimensional supersymmetric quantum field theory, extending previous methods of string theory junctions.

Contribution

It introduces a novel junction of three heterotic string theories via a specific 2D supersymmetric quantum field theory, broadening the understanding of string theory intersections.

Findings

Successfully constructs a three-way junction of heterotic strings.

Demonstrates a method involving a 2D supersymmetric quantum field theory.

Extends previous junction constructions to include non-supersymmetric theories.

Abstract

Recently, Altavista, Anastasi, Angius and Uranga discussed a method to construct junctions and bouquets of different perturbative string theories. Following this analysis, we here argue that three non-tachyonic ten-dimensional heterotic string theories can be joined together at a nine-dimensional junction. This is done by creating a two-dimensional non-conformal $\mathcal{N}{=}(0,1)$ supersymmetric quantum field theory with three asymptotic ends, each equipped with one of the worldsheet theories of the supersymmetric $E_8\times E_8$ theory, the supersymmetric $SO(32)$ theory, and the non-supersymmetric $SO(16)\times SO(16)$ theory, respectively. It is actually a special case of a more general construction involving an arbitrary $\mathbb{Z}_2$-symmetric theory $T$, its $\mathbb{Z}_2$-orbifold $T/\mathbb{Z}_2$, and the modified $\mathbb{Z}_2$-orbifold $(T\times q)/\mathbb{Z}_2$, where $q$ is a certain $\mathbb{Z}_2$-symmetric spin invertible theory.