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# Advances in Theoretical and Mathematical Physics

## Volume 12 (2008)

### Number 2

### The Topological G_{2} String

Pages: 243 – 318

DOI: http://dx.doi.org/10.4310/ATMP.2008.v12.n2.a2

#### Authors

#### 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.