Heterotic and M-theory Compactifications for String Phenomenology

Abstract

In this thesis, we explore two approaches to string phenomenology. In the first half of the work, we investigate M-theory compactifications on spaces with co-dimension four, orbifold singularities. We construct M-theory on C^2/Z_N by coupling 11-dimensional supergravity to a seven-dimensional Yang-Mills theory located on the orbifold fixed-plane. The resulting action is supersymmetric to leading non-trivial order in the 11-dim Newton constant. We thereby reduce M-theory on a G2 orbifold with C^2/Z_N singularities, explicitly incorporating the additional gauge fields at the singularities. We derive the Kahler potential, gauge-kinetic function and superpotential for the resulting N=1 four-dimensional theory. Blowing-up of the orbifold is described by a Higgs effect and the results are consistent with the corresponding ones obtained for smooth G2 spaces. Further, we consider flux and Wilson lines on singular loci of the G2 space, and discuss the relation to N=4 SYM theory. In the second half, we develop an algorithmic framework for E8 x E8 heterotic compactifications with monad bundles. We begin by considering cyclic Calabi-Yau manifolds where we classify positive monad bundles, prove stability, and compute the complete particle spectrum for all bundles. Next, we generalize the construction to bundles on complete intersection Calabi-Yau manifolds. We show that the class of positive monad bundles, subject to the heterotic anomaly condition, is finite (~7000 models). We compute the particle spectrum for these models and develop new techniques for computing the cohomology of line bundles. There are no anti-generations of particles and the spectrum is manifestly moduli-dependent. We further study the slope-stability of positive monad bundles and develop a new method for proving stability of SU(n) vector bundles.

PhD Thesis, 230 pages; University of Oxford (2008)

References in corpus (41)

• Eleven-Dimensional Supergravity on a Manifold with Boundary
• Toward Realistic Intersecting D-Brane Models
• Vector Bundles And F Theory
• Heterotic M-theory in Five Dimensions
• Supersymmetric Gauge Theories and the AdS/CFT Correspondence
• An SU(5) Heterotic Standard Model
• A Heterotic Standard Model
• On the Four-Dimensional Effective Action of Strongly Coupled Heterotic String Theory
• Gluino Condensation in Strongly Coupled Heterotic String Theory
• Heterotic GUT and Standard Model Vacua from simply connected Calabi-Yau Manifolds
• Chiral Fermions from Manifolds of $G_2$ Holonomy
• Superpotentials and Membrane Instantons
• Vector Bundles over Elliptic Fibrations
• M theory and Singularities of Exceptional Holonomy Manifolds
• Unification and Fermion Mass Structure
• On Realising N=1 Super Yang-Mills in M theory
• Heterotic Compactification, An Algorithmic Approach
• A Moduli Fixing Mechanism in M theory
• (Weak) G_2 Holonomy from Self-duality, Flux and Supersymmetry
• Exploring the Vacuum Geometry of N=1 Gauge Theories
• Moduli Dependent Spectra of Heterotic Compactifications
• Some Three Generation (0,2) Calabi-Yau Models
• Deconstruction, G_2 Holonomy, and Doublet-Triplet Splitting
• Lectures on Superstring Phenomenology
• On the Quantum Moduli Space of M Theory Compactifications
• Flux, Supersymmetry and M theory on 7-manifolds
• Higgs Doublets, Split Multiplets and Heterotic SU(3)_C x SU(2)_L x U(1)_Y Spectra
• Matter From G(2) Manifolds
• Chirality Change in String Theory
• General Metrics of G_2 Holonomy and Contraction Limits
• Compact weak G_2-manifolds with conical singularities
• Perturbative Anti-Brane Potentials in Heterotic M-theory
• Gauged D=7 Supergravity on the S**1/Z_2 Orbifold
• G_2 Domain Walls in M-theory
• Anomalies in M-theory on singular G_2-manifolds
• Four-dimensional Effective M-theory on a Singular G_2 Manifold
• M-Theory on the Orbifold C^2/Z_N
• Monads and Vector Bundles on Quadrics
• Stable bundles on 3-fold hypersurfaces
• On the semistability of instanton sheaves over certain projective varieties
• Semistability of certain bundles on a quintic Calabi-Yau threefold

Cited by in corpus (15)

• Heterotic Line Bundle Standard Models
• Exploring Positive Monad Bundles And A New Heterotic Standard Model
• Stabilizing All Geometric Moduli in Heterotic Calabi-Yau Vacua
• The Atiyah Class and Complex Structure Stabilization in Heterotic Calabi-Yau Compactifications
• Stability Walls in Heterotic Theories
• Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds
• Yukawa Couplings in Heterotic Compactification
• Geometric constraints in dual F-theory and heterotic string compactifications
• Yukawa Textures From Heterotic Stability Walls
• Transitions in the Web of Heterotic Vacua
• An Algorithmic Approach to Heterotic String Phenomenology
• Heterotic/Heterotic and Heterotic/F-theory Duality
• Vacuum Varieties, Holomorphic Bundles and Complex Structure Stabilization in Heterotic Theories
• Spectral Covers, Integrality Conditions, and Heterotic/F-theory Duality
• Yukawa Textures From Singular Spectral Data