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Aspects of N=1 Type I-Heterotic Duality in Four Dimensions

Zurab Kakushadze

TL;DR

This work analyzes N=1 Type I–heterotic duality in four dimensions by focusing on a perturbatively tractable pair where the Type I side contains only D9-branes. The authors show that the perturbative heterotic superpotential is essential to align massless spectra via Higgsing and to match moduli spaces at tree level, with anomalous U(1) playing a key role in both theories. A detailed dictionary is developed to translate perturbative effects across the dual descriptions, including how twisted and untwisted sectors map and how D5-branes/small instantons relate. The results suggest that perturbative data from Type I can inform non-perturbative heterotic dynamics and outline paths to study perturbative corrections and non-perturbative effects systematically. The analysis is organized around a Z3 orbifold construction, its heterotic dual, and the corresponding superpotential and moduli-space structures, highlighting the intricate interplay between branes, fluxes, and discrete moduli in 4D N=1 dual pairs.

Abstract

In this paper we discuss some aspects of N=1 type I-heterotic string duality in four dimensions. We consider a particular example of a (weak-weak) dual pair where on the type I side there are only D9-branes corresponding to perturbative heterotic description in a certain region of the moduli space. We match the perturbative type I and heterotic tree-level massless spectra via giving certain scalars appropriate vevs, and point out the crucial role of the perturbative superpotential (on the heterotic side) for this matching. We also discuss the role of anomalous U(1) gauge symmetry present in both type I and heterotic models. In the perturbative regime we match the (tree-level) moduli spaces of these models. Since both type I and heterotic models can be treated perturbatively, we are able to discuss a dictionary that in generic models maps type I description onto heterotic one, and vice-versa. Finally, we discuss possible directions to study perturbative quantum corrections to the moduli space, as well as outline ways to learn about the non-perturbative effects in both descriptions.

Aspects of N=1 Type I-Heterotic Duality in Four Dimensions

TL;DR

This work analyzes N=1 Type I–heterotic duality in four dimensions by focusing on a perturbatively tractable pair where the Type I side contains only D9-branes. The authors show that the perturbative heterotic superpotential is essential to align massless spectra via Higgsing and to match moduli spaces at tree level, with anomalous U(1) playing a key role in both theories. A detailed dictionary is developed to translate perturbative effects across the dual descriptions, including how twisted and untwisted sectors map and how D5-branes/small instantons relate. The results suggest that perturbative data from Type I can inform non-perturbative heterotic dynamics and outline paths to study perturbative corrections and non-perturbative effects systematically. The analysis is organized around a Z3 orbifold construction, its heterotic dual, and the corresponding superpotential and moduli-space structures, highlighting the intricate interplay between branes, fluxes, and discrete moduli in 4D N=1 dual pairs.

Abstract

In this paper we discuss some aspects of N=1 type I-heterotic string duality in four dimensions. We consider a particular example of a (weak-weak) dual pair where on the type I side there are only D9-branes corresponding to perturbative heterotic description in a certain region of the moduli space. We match the perturbative type I and heterotic tree-level massless spectra via giving certain scalars appropriate vevs, and point out the crucial role of the perturbative superpotential (on the heterotic side) for this matching. We also discuss the role of anomalous U(1) gauge symmetry present in both type I and heterotic models. In the perturbative regime we match the (tree-level) moduli spaces of these models. Since both type I and heterotic models can be treated perturbatively, we are able to discuss a dictionary that in generic models maps type I description onto heterotic one, and vice-versa. Finally, we discuss possible directions to study perturbative quantum corrections to the moduli space, as well as outline ways to learn about the non-perturbative effects in both descriptions.

Paper Structure

This paper contains 8 sections, 9 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Type I Model
  3. Heterotic String Model
  4. Superpotential
  5. Moduli Space
  6. Discrete Moduli
  7. Type I-Heterotic Dictionary
  8. Conclusions

Figures (1)

  • Figure 1: A schematic picture of the (perturbative) moduli space ${\cal M}$ (of the heterotic model). Region $A$ is the subspace corresponding to the type I model. Region $C$ is the subspace where some or all of the $S_{\alpha\beta\gamma}$ vevs are zero and some or all of the $T_{\alpha\beta\gamma}$ fields are massless. Region $B$ complements $A$ and $C$ in ${\cal M}$.