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N=1 and non-supersymmetric open string theories in six and four space-time dimensions

Lars Goerlich

TL;DR

This thesis investigates the construction of N=1 and non-supersymmetric open-string theories in six and four spacetime dimensions via orbifold and orientifold techniques. It combines a foundational treatment of orbifolds and orientifolds with three main research strands: open strings in constant EM backgrounds (revealing boundary noncommutativity and flux-induced chirality), asymmetric orientifolds (linking left-right asymmetries to noncommutative brane worldvolumes and novel spectra), and explicit phenomenological explorations of toroidal and orbifold compactifications (including sigma Omega orientifolds) that realize MSSM-like structures. A key contribution is the explicit computation of open-string commutators in general constant flux backgrounds and the demonstration that magnetic fluxes on D-branes can produce chiral spectra while preserving or breaking supersymmetry in controlled ways. The work also elucidates tadpole cancellation, boundary-state constructions, and the role of discrete torsion in shaping the closed- and open-string spectra, culminating in realistic-looking, albeit non-supersymmetric or partially supersymmetric, string vacua with potential connections to MSSM-like phenomenology.

Abstract

This thesis contains an introductory chapter on orbifolds. The following chapter explains the foundations of orientifolds. Chapters 4-7 present own research. In chapter 4 we quantize open strings with linear boundary conditions, as they show up in electro-magnetic fields. We quantize the zero-modes for toroidal compactifications, too. As an application we calculate the commutator of the coordinate fields in the case of general constant Neveu-Schwarz U(1)-field strengths. Thereby we confirm previous results on non-commutativity of open string theories in Neveu-Schwarz backgrounds. Chapter 5 reviews the results of a former publication [1] on asymmetric orientifolds, supplemented by some recent insights in connection with chapter 4. Chapter 6 summarizes publication [2] where we investigated to what extend one can build phenomenologically interesting models from toroidal orientifolds. By turning on magnetic fluxes on D9-branes we induce chiral fermions. Most calculations are performed in an (equivalent) T-dual picture. Here the number of chiral fermions is given by the topological intersection number of D-branes. In orientifolds of toroidal compactifications one obtains either non-chiral or non-supersymmetric orientifold solutions. However both properties can be reconciled in orientifolds that are obtained from specific supersymmetric orbifold compactifications. In chapter 7 we present the ``sigma Omega'' -Orientifold on a T^6/Z(4) orbifold. As a very attractive example we investigate a supersymmetric U(4) x U(2)^3_L x U(2)^3_R model that is broken to an MSSM-like model by switching on suitable background fields in the LEEA. This chapter is based on our publication [3]. An appendix is supplemented with formulas applied in the text, as well as proofs to two theorems.

N=1 and non-supersymmetric open string theories in six and four space-time dimensions

TL;DR

This thesis investigates the construction of N=1 and non-supersymmetric open-string theories in six and four spacetime dimensions via orbifold and orientifold techniques. It combines a foundational treatment of orbifolds and orientifolds with three main research strands: open strings in constant EM backgrounds (revealing boundary noncommutativity and flux-induced chirality), asymmetric orientifolds (linking left-right asymmetries to noncommutative brane worldvolumes and novel spectra), and explicit phenomenological explorations of toroidal and orbifold compactifications (including sigma Omega orientifolds) that realize MSSM-like structures. A key contribution is the explicit computation of open-string commutators in general constant flux backgrounds and the demonstration that magnetic fluxes on D-branes can produce chiral spectra while preserving or breaking supersymmetry in controlled ways. The work also elucidates tadpole cancellation, boundary-state constructions, and the role of discrete torsion in shaping the closed- and open-string spectra, culminating in realistic-looking, albeit non-supersymmetric or partially supersymmetric, string vacua with potential connections to MSSM-like phenomenology.

Abstract

This thesis contains an introductory chapter on orbifolds. The following chapter explains the foundations of orientifolds. Chapters 4-7 present own research. In chapter 4 we quantize open strings with linear boundary conditions, as they show up in electro-magnetic fields. We quantize the zero-modes for toroidal compactifications, too. As an application we calculate the commutator of the coordinate fields in the case of general constant Neveu-Schwarz U(1)-field strengths. Thereby we confirm previous results on non-commutativity of open string theories in Neveu-Schwarz backgrounds. Chapter 5 reviews the results of a former publication [1] on asymmetric orientifolds, supplemented by some recent insights in connection with chapter 4. Chapter 6 summarizes publication [2] where we investigated to what extend one can build phenomenologically interesting models from toroidal orientifolds. By turning on magnetic fluxes on D9-branes we induce chiral fermions. Most calculations are performed in an (equivalent) T-dual picture. Here the number of chiral fermions is given by the topological intersection number of D-branes. In orientifolds of toroidal compactifications one obtains either non-chiral or non-supersymmetric orientifold solutions. However both properties can be reconciled in orientifolds that are obtained from specific supersymmetric orbifold compactifications. In chapter 7 we present the ``sigma Omega'' -Orientifold on a T^6/Z(4) orbifold. As a very attractive example we investigate a supersymmetric U(4) x U(2)^3_L x U(2)^3_R model that is broken to an MSSM-like model by switching on suitable background fields in the LEEA. This chapter is based on our publication [3]. An appendix is supplemented with formulas applied in the text, as well as proofs to two theorems.

Paper Structure

This paper contains 109 sections, 1 theorem, 615 equations, 37 figures, 29 tables.

Table of Contents

  1. Introduction
  2. String theory
  3. Quantization of classical strings
  4. String theory as a theory of quantum gravity
  5. Supersymmetric string theories
  6. Compactifications
  7. Open strings and unoriented string theories
  8. Chiral fermions in open string theories
  9. Orbifolds
  10. General construction of orbifolds
  11. Torus compactification as an orbifold
  12. Moduli-space of toroidal compactifications, T-duality group and symmetries
  13. Compactification on T², T-duality and symmetries
  14. Points of enhanced symmetry in the moduli space $SO(2,2,\mathbb{R})$
  15. The world-sheet-parity on T²
  16. ...and 94 more sections

Key Result

Theorem 1

A finite dimensional Lorentz transformation $\Lambda\in SO(1,n)$ preserving the corresponding metric $G$ admits $n+1$ Eigenvectors, if there are no single light-like Eigenvectors with Eigenvalue $\pm1$. (This is a sufficient but, not a necessary condition). In this case $n-1$ of the Eigenvalues and

Figures (37)

  • Figure 1: Closed-string (blue) evolving in time. The world-sheet, which is a classical solution is indicated in transparent orange.
  • Figure 2: Open-string (blue) evolving in time. Both world-sheet boundaries (green) belong to the same stack of D-branes. This classical solution can be associated with a gauge-boson of the quantized theory.
  • Figure 3: First three terms of the string perturbation series with four external closed string states involved
  • Figure 4: Perturbative expansion of electron-electron scattering in QED with one fermion generation.
  • Figure 5: Open-string with Chan-Paton charges $n$ and $\bar{n}$
  • ...and 32 more figures

Theorems & Definitions (2)

  • Definition 1
  • Theorem 1