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4-D Chiral N=1 Type I Vacua With And Without D5-Branes

Zurab Kakushadze, Gary Shiu

TL;DR

This work develops a prescription for constructing four-dimensional $N=1$ Type I vacua on Abelian orbifolds, focusing on models with D9-branes and extending to configurations with D5-branes. It analyzes tadpole cancellation and the Type I–heterotic duality, emphasizing how anomalous $U(1)$ dynamics and perturbative superpotentials drive blow-up processes that align massless spectra across dual descriptions. The authors provide explicit realizations on $Z_3\times Z_3$ and $Z_6$ orbifolds, detailing gauge groups and chiral content, and discuss how heterotic duals reproduce the same physics, including non-perturbative aspects on the Type I side. The paper also maps the perturbative moduli spaces of the dual theories, highlighting the necessity of dilaton mixing and D-term-induced Higgsing to achieve precise spectral matching.

Abstract

In this paper we consider compactifications of type I strings on Abelian orbifolds. We discuss the tadpole cancellation conditions for the general case with D9-branes only. Such compactifications have (perturbative) heterotic duals which are also realized as orbifolds (with non-standard embedding of the gauge connection). The latter have extra twisted states that become massive once orbifold singularities are blown-up. This is due to the presence of perturbative heterotic superpotential with couplings between the extra twisted states, the orbifold blow-up modes, and (sometimes) untwisted matter fields. Anomalous U(1) (generically present in such models) also plays an important role in type I-heterotic (tree-level) duality matching. We illustrate these issues on a particular example of Z_3 \otimes Z_3 orbifold type I model (and its heterotic dual). The model has N=1 supersymmetry, U(4)^3 \otimes SO(8) gauge group, and chiral matter. We also consider compactifications of type I strings on Abelian orbifolds with both D9- and D5-branes. We discuss tadpole cancellation conditions for a certain class of such models. We illustrate the model building by considering a particular example of type I theory compactified on Z_6 orbifold. The model has N=1 supersymmetry, [U(6)\otimes U(6)\otimes U(4)]^2 gauge group, and chiral matter. This would correspond to a non-perturbative chiral vacuum from the heterotic point of view.

4-D Chiral N=1 Type I Vacua With And Without D5-Branes

TL;DR

This work develops a prescription for constructing four-dimensional Type I vacua on Abelian orbifolds, focusing on models with D9-branes and extending to configurations with D5-branes. It analyzes tadpole cancellation and the Type I–heterotic duality, emphasizing how anomalous dynamics and perturbative superpotentials drive blow-up processes that align massless spectra across dual descriptions. The authors provide explicit realizations on and orbifolds, detailing gauge groups and chiral content, and discuss how heterotic duals reproduce the same physics, including non-perturbative aspects on the Type I side. The paper also maps the perturbative moduli spaces of the dual theories, highlighting the necessity of dilaton mixing and D-term-induced Higgsing to achieve precise spectral matching.

Abstract

In this paper we consider compactifications of type I strings on Abelian orbifolds. We discuss the tadpole cancellation conditions for the general case with D9-branes only. Such compactifications have (perturbative) heterotic duals which are also realized as orbifolds (with non-standard embedding of the gauge connection). The latter have extra twisted states that become massive once orbifold singularities are blown-up. This is due to the presence of perturbative heterotic superpotential with couplings between the extra twisted states, the orbifold blow-up modes, and (sometimes) untwisted matter fields. Anomalous U(1) (generically present in such models) also plays an important role in type I-heterotic (tree-level) duality matching. We illustrate these issues on a particular example of Z_3 \otimes Z_3 orbifold type I model (and its heterotic dual). The model has N=1 supersymmetry, U(4)^3 \otimes SO(8) gauge group, and chiral matter. We also consider compactifications of type I strings on Abelian orbifolds with both D9- and D5-branes. We discuss tadpole cancellation conditions for a certain class of such models. We illustrate the model building by considering a particular example of type I theory compactified on Z_6 orbifold. The model has N=1 supersymmetry, [U(6)\otimes U(6)\otimes U(4)]^2 gauge group, and chiral matter. This would correspond to a non-perturbative chiral vacuum from the heterotic point of view.

Paper Structure

This paper contains 9 sections, 25 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Type I String on ${\bf Z}_3 \otimes {\bf Z}_3$ Orbifold
  3. Heterotic String on ${\bf Z}_3 \otimes {\bf Z}_3$ Orbifold
  4. Superpotential
  5. Moduli Space
  6. Type I String on ${\bf Z}_6$ Orbifold
  7. Conclusions
  8. Tadpoles for $D9$-branes
  9. Tadpoles for $D9$- and $D5$-branes

Figures (1)

  • Figure 1: A schematic picture of the (perturbative) moduli space ${\cal M}$ of the heterotic ${\bf Z}_3 \otimes {\bf Z}_3$ orbifold. This figure is taken from Ref [2] where the ${\bf Z}_3$ orbifold is discussed since the schematic picture of the moduli space for both ${\bf Z}_3$ and ${\bf Z}_3 \otimes {\bf Z}_3$ orbifolds are the same. 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 $T_{\alpha\beta\gamma}$ and $T^{a\pm}_{\alpha\beta}$ fields are massless. Region $B$ complements $A$ and $C$ in ${\cal M}$.