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super topological recursion
Vincent Bouchard1, Kento Osuga2,3
1Department of Mathematics and Statistical Sciences, University of Alberta, 632 CAB, Edmonton, AB T6G 2G1 Canada.
Letters in Mathematical Physics
|December 13, 2021
Summary
We present abstract super loop equations and two novel methods for their solution. These approaches generalize topological recursion and utilize super Airy structures for calculations in 2d supergravity.
Area of Science:
- Theoretical Physics
- Mathematical Physics
Background:
- Topological recursion is a powerful tool in mathematical physics.
- The study of 2d supergravity requires advanced computational methods.
Purpose of the Study:
- Introduce abstract super loop equations.
- Provide two novel, equivalent methods for solving these equations.
- Extend existing formalisms to supersymmetric contexts.
Main Methods:
- A recursive formalism generalizing Eynard-Orantin topological recursion.
- A method based on the framework of super Airy structures.
- Utilizing the geometry of a local super spectral curve.
Main Results:
- The development of a supersymmetric generalization of topological recursion.
- The establishment of two equivalent solution pathways for abstract super loop equations.
- A framework for computing correlation functions in 2d supergravity.
Conclusions:
- The introduced methods offer new ways to tackle problems in 2d supergravity.
- The abstract super loop equations provide a unified framework for related problems.
- These findings advance the computational tools in supersymmetric field theories.
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