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

Yuji Tachikawa

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.

On the trivalent junction of three non-tachyonic heterotic string 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 supersymmetric quantum field theory with three asymptotic ends, each equipped with one of the worldsheet theories of the supersymmetric theory, the supersymmetric theory, and the non-supersymmetric theory, respectively. It is actually a special case of a more general construction involving an arbitrary -symmetric theory , its -orbifold , and the modified -orbifold , where is a certain -symmetric spin invertible theory.

Paper Structure

This paper contains 5 sections, 8 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Objective
  3. Strategy
  4. Construction
  5. Discussions

Figures (1)

  • Figure 1: Schematic picture of the junction. Each line represents an $\mathcal{N}{=}(0,1)$ chiral multiplet parameterizing an asymptotic region, together with the internal theory indicated there. The central blob has interactions that connect the three regions.