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arXiv · 1812.02505

A Klein TQFT: the local Real Gromov-Witten theory of curves

Penka Georgieva·Eleny-Nicoleta Ionel
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Abstract

In this paper we study the Real Gromov-Witten theory of local 3-folds over Real curves. We show that this gives rise to a 2-dimensional Klein TQFT defined on an extension of the category of unorientable surfaces. We use this structure to completely solve the theory by providing a closed formula for the local RGW invariants in terms of representation theoretic data, extending earlier results of Bryan and Pandharipande. As a consequence we obtain the local version of the real Gopakumar-Vafa formula that expresses the connected real Gromov-Witten invariants in terms of integer invariants. In the case of the resolved conifold the partition function of the RGW invariants agrees with that of the SO/Sp Chern-Simons theory.

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Penka Georgieva, Eleny-Nicoleta Ionel. 2018-12-06. A Klein TQFT: the local Real Gromov-Witten theory of curves. https://doi.org/10.1016/j.aim.2021.107972

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