[Formula: see text] super topological recursion

Vincent Bouchard; Kento Osuga

doi:10.1007/s11005-021-01479-x

$N = 1$ super topological recursion

Lett Math Phys. 2021;111(6):144. doi: 10.1007/s11005-021-01479-x. Epub 2021 Nov 26.

Authors

Vincent Bouchard¹, Kento Osuga^{2

3}

Affiliations

¹ Department of Mathematics and Statistical Sciences, University of Alberta, 632 CAB, Edmonton, AB T6G 2G1 Canada.
² School of Mathematics and Statistics, University of Sheffield, The Hicks Building, Hounsfield Road, Sheffield, S3 7RH UK.
³ Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland.

Abstract

We introduce the notion of $N = 1$ 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.