The Topological G2 String

Abstract

We construct new topological theories related to sigma models whose target space is a seven dimensional manifold of G_2 holonomy. We define a new type of topological twist and identify the BRST operator and the physical states. Unlike the more familiar six dimensional case, our topological model is defined in terms of conformal blocks and not in terms of local operators of the original theory. We also present evidence that one can extend this definition to all genera and construct a seven-dimensional topological string theory. We compute genus zero correlation functions and relate these to Hitchin's functional for three-forms in seven dimensions. Along the way we develop the analogue of special geometry for G_2 manifolds. When the seven dimensional topological twist is applied to the product of a Calabi-Yau manifold and a circle, the result is an interesting combination of the six dimensional A- and B-models.

76 pages, 1 figure, typos corrected

References in corpus (13)

• Black Hole Attractors and the Topological String
• The effective action of Type IIA Calabi-Yau orientifolds
• M theory and Singularities of Exceptional Holonomy Manifolds
• N=2 strings and the twistorial Calabi-Yau
• Attractors and the Holomorphic Anomaly
• The Hitchin functionals and the topological B-model at one loop
• Generalised $G_2$-manifolds
• Topological Open String Amplitudes On Orientifolds
• Special metric structures and closed forms
• Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds
• Topological M-theory as Unification of Form Theories of Gravity
• Domain Walls, Hitchin's Flow Equations and G_2-Manifolds
• Topological M Theory from Pure Spinor Formalism

Cited by in corpus (13)

• Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops
• Open G2 Strings
• Membranes for Topological M-Theory
• A Note on Topological M5-branes and String-Fivebrane Duality
• G2 Hitchin functionals at one loop
• On the symmetries of special holonomy sigma models
• AKSZ constructions for topological membranes on $G_2$-manifolds
• Toric Geometry and String Theory
• Conjectures on counting associative 3-folds in $G_2$-manifolds
• Topological membrane theory from Mathai-Quillen formalism
• Mirror symmetry aspects for compact G_2 manifolds
• Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings
• Deformed Shatashvili-Vafa algebra for superstrings on AdS${}_3\times {\mathcal{M}}_7$