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To Tilt or Not To Tilt: Discrete Gauge Symmetries in Global Intersecting D-Brane Models

Gabriele Honecker, Wieland Staessens

TL;DR

The paper derives complete Zn discrete gauge symmetry conditions for global intersecting D6-brane models on toroidal orbifolds, incorporating tilted tori and non-unimodular cycle lattices. It develops a two-layer framework linking massless U(1) remnants, axion couplings, and D2-instanton effects to a set of homological Zn constraints, and applies it to explicit Left-Right Symmetric and Pati-Salam global models to uncover stringy Zn symmetries such as Z2, Z4, and Z6. It shows that some field-theoretic expectations (e.g., R-parity, baryon-triality, proton-hexality) can be absent or altered in string constructions, while new, model-dependent discrete symmetries can arise, sometimes with generation dependence. The results illuminate how discrete gauge symmetries in string vacua influence perturbative and non-perturbative couplings, selection rules, and potential phenomenological implications for proton stability and MSSM-like low-energy theories.

Abstract

Discrete gauge symmetries in global intersecting D-brane models constrain the exact form of the perturbative as well as non-perturbative superpotential. We derive the complete set of conditions on the existence of discrete Zn gauge symmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional or rigid D6-branes on tilted tori, for which global models of particle physics are known. Several examples of global left-right symmetric and Pati-Salam models are presented. Some discrete `stringy' Zn symmetries are trivial from the field theory point of view, while others have not been identified before.

To Tilt or Not To Tilt: Discrete Gauge Symmetries in Global Intersecting D-Brane Models

TL;DR

The paper derives complete Zn discrete gauge symmetry conditions for global intersecting D6-brane models on toroidal orbifolds, incorporating tilted tori and non-unimodular cycle lattices. It develops a two-layer framework linking massless U(1) remnants, axion couplings, and D2-instanton effects to a set of homological Zn constraints, and applies it to explicit Left-Right Symmetric and Pati-Salam global models to uncover stringy Zn symmetries such as Z2, Z4, and Z6. It shows that some field-theoretic expectations (e.g., R-parity, baryon-triality, proton-hexality) can be absent or altered in string constructions, while new, model-dependent discrete symmetries can arise, sometimes with generation dependence. The results illuminate how discrete gauge symmetries in string vacua influence perturbative and non-perturbative couplings, selection rules, and potential phenomenological implications for proton stability and MSSM-like low-energy theories.

Abstract

Discrete gauge symmetries in global intersecting D-brane models constrain the exact form of the perturbative as well as non-perturbative superpotential. We derive the complete set of conditions on the existence of discrete Zn gauge symmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional or rigid D6-branes on tilted tori, for which global models of particle physics are known. Several examples of global left-right symmetric and Pati-Salam models are presented. Some discrete `stringy' Zn symmetries are trivial from the field theory point of view, while others have not been identified before.

Paper Structure

This paper contains 21 sections, 65 equations, 12 tables.

Table of Contents

  1. Introduction
  2. Discrete Gauge Symmetries
  3. Conditions on the existence of discrete $\mathbb{Z}_n$ symmetries in intersecting D6-brane worlds
  4. $\mathbb{Z}_n$ action on closed string axions and D2-brane instantons
  5. Discrete $\mathbb{Z}_n$ symmetries versus centers of non-Abelian gauge groups
  6. Discrete $\mathbb{Z}_n$ symmetries on fractional D6-branes in toroidal orbifold models
  7. The orbifold $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2 \times \Omega\mathcal{R})$ without discrete torsion on tilted tori
  8. The orbifold $T^6/(\mathbb{Z}_6 \times \Omega\mathcal{R})$ with AAB lattice
  9. The $T^6/(\mathbb{Z}_6' \times \Omega\mathcal{R})$ with ABa lattice
  10. The orbifold $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_6' \times \Omega\mathcal{R})$ with discrete torsion and AAA lattice
  11. Discrete $\mathbb{Z}_n$ symmetries in supersymmetric field theories
  12. Global Intersecting D-Brane Models
  13. Left-right symmetric models
  14. A global model on $T^6/(\mathbb{Z}_6 \times \Omega\mathcal{R})$
  15. A global model on $T^6/(\mathbb{Z}_6' \times \Omega\mathcal{R})$ without a hidden sector
  16. ...and 6 more sections