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Discrete Wilson Lines in N=1 D=4 Type IIB Orientifolds: A Systematic Exploration for $\IZ_6$ Orientifold

Mirjam Cvetic, Angel M. Uranga, Jing Wang

TL;DR

The paper addresses constructing general discrete Wilson lines in four-dimensional $N=1$ Type IIB orientifolds, focusing on the $f Z_6$ case and using a T-dual brane-at-fixed-points picture to enforce algebraic and RR tadpole consistency. It develops explicit order-3 and order-2 Wilson lines, and a continuous Wilson line, and uncovers that tadpole conditions in the original and T-dual pictures are related by a discrete Fourier transform, enabling efficient model-building. A systematic search reveals only a few inequivalent models; among them, two classes yield semi-realistic gauge structures with branes at $f Z_6$ fixed points, including a left-right symmetric group and a Pati-Salam-like scenario when anti-branes are included. The work provides complete spectra and Yukawa couplings for the viable classes, demonstrating potential routes to realistic-like sectors within a controlled string-theoretic framework, and offers techniques applicable to other orientifolds.

Abstract

We develop techniques to construct general discrete Wilson lines in four-dimensional N=1 Type IIB orientifolds, their T-dual realization corresponds to branes positioned at the orbifold fixed points. The explicit order two and three Wilson lines along with their tadpole consistency conditions are given for D=4 N=1 Z_6 Type IIB orientifold. The systematic search for all models with general order three Wilson lines leads to a small class of inequivalent models. There are only two inequivalent classes of a potentially phenomenologically interesting model that has a possible SU(3)_{color} x SU(2)_L x SU(2)_R x U(1)_{B-L} gauge structure, arising from a set of branes located at the Z_6 orbifold fixed point. We calculate the spectrum and Yukawa couplings for this model. On the other hand, introduction of anti-branes allows for models with three families and realistic gauge group assignment, arising from branes located at the Z_3 orbifold fixed points.

Discrete Wilson Lines in N=1 D=4 Type IIB Orientifolds: A Systematic Exploration for $\IZ_6$ Orientifold

TL;DR

The paper addresses constructing general discrete Wilson lines in four-dimensional Type IIB orientifolds, focusing on the case and using a T-dual brane-at-fixed-points picture to enforce algebraic and RR tadpole consistency. It develops explicit order-3 and order-2 Wilson lines, and a continuous Wilson line, and uncovers that tadpole conditions in the original and T-dual pictures are related by a discrete Fourier transform, enabling efficient model-building. A systematic search reveals only a few inequivalent models; among them, two classes yield semi-realistic gauge structures with branes at fixed points, including a left-right symmetric group and a Pati-Salam-like scenario when anti-branes are included. The work provides complete spectra and Yukawa couplings for the viable classes, demonstrating potential routes to realistic-like sectors within a controlled string-theoretic framework, and offers techniques applicable to other orientifolds.

Abstract

We develop techniques to construct general discrete Wilson lines in four-dimensional N=1 Type IIB orientifolds, their T-dual realization corresponds to branes positioned at the orbifold fixed points. The explicit order two and three Wilson lines along with their tadpole consistency conditions are given for D=4 N=1 Z_6 Type IIB orientifold. The systematic search for all models with general order three Wilson lines leads to a small class of inequivalent models. There are only two inequivalent classes of a potentially phenomenologically interesting model that has a possible SU(3)_{color} x SU(2)_L x SU(2)_R x U(1)_{B-L} gauge structure, arising from a set of branes located at the Z_6 orbifold fixed point. We calculate the spectrum and Yukawa couplings for this model. On the other hand, introduction of anti-branes allows for models with three families and realistic gauge group assignment, arising from branes located at the Z_3 orbifold fixed points.

Paper Structure

This paper contains 12 sections, 93 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Wilson lines in the $\bf Z_6$ orientifold
  3. Order Three Wilson lines
  4. Order two Wilson lines
  5. Continuous Wilson line in a $\bf Z_6$ plane
  6. Tadpole Cancellation Conditions
  7. Spectrum
  8. Models
  9. Systematic Construction of Models
  10. A semi-realistic model
  11. A semi-realistic model with anti-branes
  12. Conclusions

Figures (1)

  • Figure 1: Structure of $T^6/\bf Z_6$ modded out by $\Omega_3$. At each $\theta^2$ fixed point we have indicated the $\theta^2$-twisted crosscap tadpole. This has to be canceled by including D3-branes (denoted by crosses) and D7$_3$-branes (depicted as planes) sitting or passing through those points.