Algebroids, Heterotic Moduli Spaces and the Strominger System

Abstract

In this paper we study compactifications of heterotic string theory on manifolds satisfying the ddbar-lemma. We consider the Strominger system description of the low energy supergravity to first order in alpha' and show that the moduli of such compactifications are subspaces of familiar cohomology groups such as H^1(TX), H^1(TX*), H^1(End_0(V)) and H^1(End_0(TX)). These groups encode the complex structure, Kahler moduli, bundle moduli and perturbations of the spin connection respectively in the case of a Calabi-Yau compactification. We investigate the fluctuations of only a subset of the conditions of the Strominger system (expected to correspond physically to F-term constraints in the effective theory). The full physical moduli space is, therefore, given by a further restriction on these degrees of freedom which we discuss but do not explicitly provide. This paper is complementary to a previous tree-level worldsheet analysis of such moduli and agrees with that discussion in the limit of vanishing alpha'. The structure we present can be interpreted in terms of recent work in Atiyah and Courant algebroids, and we conjecture links with aspects of Hitchin's generalized geometry to heterotic moduli.

33 pages

References in corpus (20)

• The gauge algebra of double field theory and Courant brackets
• Generalized complex geometry
• Double Field Theory Formulation of Heterotic Strings
• Lectures on Generalized Complex Geometry for Physicists
• Anomaly Cancellation and Smooth Non-Kahler Solutions in Heterotic String Theory
• Torsional Heterotic Geometries
• Stabilizing All Geometric Moduli in Heterotic Calabi-Yau Vacua
• On the $\partial \overline{\partial }$-Lemma and Bott-Chern cohomology
• Stabilizing the Complex Structure in Heterotic Calabi-Yau Vacua
• Non-Kaehler Heterotic String Compactifications with non-zero fluxes and constant dilaton
• Generalized geometry and the Hodge decomposition
• Dimensional Reduction of the Heterotic String over nearly-Kaehler manifolds
• Generalized Kahler geometry
• The ${\alpha }^{\prime }$ Expansion On A Compact Manifold Of Exceptional Holonomy
• G-structures and Domain Walls in Heterotic Theories
• Heterotic Flux Vacua from Hybrid Linear Models
• Orbifold Phases of Heterotic Flux Vacua
• Infinitesimal Symmetries of Dixmier-Douady Gerbes
• Cohomological aspects of non-Kähler manifolds
• The first Pontryagin class

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• The quaternionic Heisenberg group and Heterotic String Solutions with non-constant dilaton in dimensions 7 and 5
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• $T^4$ fibrations over Calabi-Yau two-folds and non-Kahler manifolds in string theory
• $Spin(7)$ Compactifications and 1/4-BPS Vacua in Heterotic Supergravity