Abstract
We study the topological G2 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 G2 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.
Highlights
Topological string models with Calabi-Yau target spaces provide us with subsectors of string theory in which certain quantities can be computed exactly
In outline, starting with an O(d, d)×R+ generalised geometry description of the target space, we show that supersymmetry implies the existence of a torsion-free G × G structures
We show that the operators are nilpotent and commute in the correct manner if the generalised connection is torsion-free, which implies that the underlying string background is an NSNS Minkowski solution preserving at least N = 1 supersymmetry
Summary
Topological string models with Calabi-Yau target spaces provide us with subsectors of string theory in which certain quantities can be computed exactly. An attempt at constructing this theory was made in [11], where a targetspace action was proposed by starting from a Hitchin functional for a generalised G2 × G2 structure In this case, the 1-loop partition function of the topological G2 string disagreed with the target-space calculation, differing by a factor of the Ray-Singer torsion of the background G2 manifold. The central result of [9] was the construction of a target-space theory based on an extended Hitchin functional for SL(3, C) whose BV quantisation gives precisely the 1-loop partition function of the B-model on a Calabi-Yau target. We conjecture that the 1-loop partition function of the corresponding topological string is given by a certain alternating product of determinants of the Laplace operators acting on the double complex. The appendices contain our conventions and useful identities, a discussion of determinants and partition functions, and a quick review of O(d, d) × R+ generalised geometry
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