Comments on Heterotic Flux Compactifications

Abstract

In heterotic flux compactification with supersymmetry, three different connections with torsion appear naturally, all in the form $\omega +aH$. Supersymmetry condition carries $a=-1$, the Dirac operator has $a=-1/3$, and higher order term in the effective action involves $a=1$. With a view toward the gauge sector, we explore the geometry with such torsions. After reviewing the supersymmetry constraints and finding a relation between the scalar curvature and the flux, we derive the squared form of the zero mode equations for gauge fermions. With $\d H=0$, the operator has a positive potential term, and the mass of the unbroken gauge sector appears formally positive definite. However, this apparent contradiction is avoided by a no-go theorem that the compactification with $H\ne 0$ and $\d H=0$ is necessarily singular, and the formal positivity is invalid. With $\d H\neq 0$, smooth compactification becomes possible. We show that, at least near smooth supersymmetric solution, the size of $H^2$ should be comparable to that of $\d H$ and the consistent truncation of action has to keep ${\alpha }^{\prime }{R}^2$ term. A warp factor equation of motion is rewritten with ${\alpha }^{\prime }{R}^2$ contribution included precisely, and some limits are considered.

31 pages, a numerical factor corrected

References in corpus (30)

• A Large Mass Hierarchy from a Small Extra Dimension
• de Sitter Vacua in String Theory
• Hierarchies from Fluxes in String Compactifications
• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• Supergravity description of field theories on curved manifolds and a no go theorem
• CFT's From Calabi-Yau Four-folds
• M Theory, Orientifolds and G-Flux
• Flux compactifications in string theory: a comprehensive review
• The statistics of string/M theory vacua
• Distributions of flux vacua
• M-Theory on Eight-Manifolds
• Moduli Stabilization from Fluxes in a Simple IIB Orientifold
• Non-Kaehler String Backgrounds and their Five Torsion Classes
• Counting Flux Vacua
• Superstrings with Intrinsic Torsion
• Generalized structures of N=1 vacua
• Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds
• Scales and hierarchies in warped compactifications and brane worlds
• Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion
• Compactifications of Heterotic Theory on Non-Kahler Complex Manifolds: I
• Compactifications of Heterotic Strings on Non-Kahler Complex Manifolds: II
• Mirror symmetric SU(3)-structure manifolds with NS fluxes
• Heterotic String Theory on non-Kaehler Manifolds with H-Flux and Gaugino Condensate
• A no-go theorem for string warped compactifications
• The spinorial geometry of supersymmetric heterotic string backgrounds
• Supersymmetric compactifications of heterotic strings with fluxes and condensates
• AdS Strings with Torsion: Non-complex Heterotic Compactifications
• Heterotic Flux Compactifications and Their Moduli
• Anomaly, Fluxes and (2,0) Heterotic-String Compactifications
• Spinors on manifolds with boundary: APS index theorems with torsion

Cited by in corpus (22)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Flux Compactification
• Torsion-free generalized connections and Heterotic Supergravity
• Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton
• Local Heterotic Torsional Models
• Linear Sigma Models with Torsion
• Flux backgrounds from Twists
• Moduli Space of Torsional Manifolds
• Moduli Stabilising in Heterotic Nearly Kähler Compactifications
• Index Theorems on Torsional Geometries
• Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton
• Hyper-Kähler with Torsion, T-duality, and Defect (p,q) Five-branes
• Double-Scaling Limit of Heterotic Bundles and Dynamical Deformation in CFT
• Chiral Generations on Intersecting 5-branes in Heterotic String Theory
• A Note on Heterotic Dualities via M-theory
• Chiral Zero Modes on Intersecting Heterotic 5-branes
• A Heterotic Flux Background and Calibrated Five-Branes
• AdS Vacua, Attractor Mechanism and Generalized Geometries
• Family Unification via Quasi-Nambu-Goldstone Fermions in String Theory
• Solitons and Yukawa Couplings in Nearly Kahler Flux Compactifications
• Supersymmetric heterotic solutions via non-SU(3) standard embedding
• T-duality on Almost Hermitian Spaces