Abstract
We define new topological theories related to sigma models whose target space is a 7 dimensional manifold of G 2 holonomy. We show how to define the topological twist and identify the BRST operator and the physical states. Correlation functions at genus zero are computed and related to Hitchin’s topological action for three-forms. We conjecture that one can extend this definition to all genus and construct a seven-dimensional topological string theory. In contrast to the four-dimensional case, it does not seem to compute terms in the low-energy effective action in three dimensions.
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de Boer, J., Naqvi, A., Shomer, A. (2005). Towards a Topological \( \mathcal{G}_2\) String. In: Baulieu, L., de Boer, J., Pioline, B., Rabinovici, E. (eds) String Theory: From Gauge Interactions to Cosmology. NATO Science Series II: Mathematics, Physics and Chemistry, vol 208. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3733-3_5
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DOI: https://doi.org/10.1007/1-4020-3733-3_5
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