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• Published in: Letters in mathematical physics Vol. 111; no. 6
• Main Authors: Bouchard, Vincent, Osuga, Kento
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-01-2021
• ISSN: 0377-9017; 1573-0530
• DOI: 10.1007/s11005-021-01479-x

We introduce the notion of
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\begin{document}$${\mathcal {N}}=1$$\end{document}
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abstract super loop equations and provide two equivalent ways of solving them. The first approach is a recursive formalism that can be thought of as a supersymmetric generalization of the Eynard–Orantin topological recursion, based on the geometry of a local super spectral curve. The second approach is based on the framework of super Airy structures. The resulting recursive formalism can be applied to compute correlation functions for a variety of examples related to 2d supergravity.