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

Anthony Ashmore (1) , André Coimbra , Charles Strickland-Constable , Eirik Eik Svanes , David Tennyson

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Mots clés: Differential and Algebraic Geometry; Flux Compactifications; Topological Strings; Superstring Vacua; string: topological; partition function; string model; background: supersymmetry; torsion; double field theory; loop integral: 1; holonomy: G(2); Spin(7)

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

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. Journal of High Energy Physics, 2022, 02, pp.089. ⟨10.1007/JHEP02(2022)089⟩. ⟨hal-03335430⟩