# Topological G$_{2}$ and Spin(7) strings at 1-loop from double complexes

Abstract : We study the topological $G_2$ and $Spin(7)$ strings at 1-loop. We define new double complexes for supersymmetric NSNS backgrounds of string theory using generalised geometry. The 1-loop partition function then has a target-space interpretation as a particular alternating product of determinants of Laplacians, which we have dubbed the analytic torsion. In the case without flux where these backgrounds have special holonomy, we reproduce the worldsheet calculation of the $G_2$ string and give a new prediction for the $Spin(7)$ string. We also comment on connections with topological strings on Calabi-Yau and K3 backgrounds.
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https://hal.archives-ouvertes.fr/hal-03335430
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Submitted on : Monday, September 6, 2021 - 11:12:48 AM
Last modification on : Wednesday, September 8, 2021 - 9:28:34 AM

### Citation

Anthony Ashmore, André Coimbra, Charles Strickland-Constable, Eirik Eik Svanes, David Tennyson. Topological G$_{2}$ and Spin(7) strings at 1-loop from double complexes. 2021. ⟨hal-03335430⟩

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