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Summary
The article discusses the relationship between super volumes and KdV tau functions, specifically the generalized Brézin-Gross-Witten (BGW) tau function. The authors prove that the super Weil-Petersson volumes of the moduli space of super curves with Neveu-Schwarz and Ramond punctures are related to the generalized BGW tau function.
Highlights
- The generalized BGW tau function is a one-parameter deformation of the BGW tau function.
- The super Weil-Petersson volumes are related to the generalized BGW tau function.
- The authors use the Virasoro constraints to prove the relationship between the super volumes and the generalized BGW tau function.
- The generalized BGW tau function is a tau function of the KdV hierarchy.
- The authors use the spectral curve topological recursion to calculate the super volumes.
- The super volumes satisfy the Stanford-Witten recursion.
- The authors prove that the generalized BGW tau function is a generating function for the intersection numbers of the moduli space of curves.
Key Insights
- The generalized BGW tau function is a key object in the study of super volumes and the moduli space of curves. It is a one-parameter deformation of the BGW tau function, which is a well-known object in the study of matrix models and topological recursion.
- The super Weil-Petersson volumes are an important object in the study of super geometry and the moduli space of curves. They are related to the generalized BGW tau function, which provides a new perspective on these volumes.
- The Virasoro constraints are a powerful tool in the study of tau functions and the moduli space of curves. They provide a way to prove relationships between different objects, such as the super volumes and the generalized BGW tau function.
- The spectral curve topological recursion is a method for calculating the super volumes and other objects related to the moduli space of curves. It is based on the idea of using a spectral curve to encode the information about the moduli space.
- The Stanford-Witten recursion is a recursion relation that is satisfied by the super volumes. It is an important tool in the study of super geometry and the moduli space of curves.
- The generalized BGW tau function is a generating function for the intersection numbers of the moduli space of curves. This provides a new perspective on these intersection numbers and the moduli space of curves.
- The relationship between the super volumes and the generalized BGW tau function provides a new insight into the study of super geometry and the moduli space of curves. It highlights the importance of the generalized BGW tau function in this field.
Mindmap
Citation
Alexandrov, A., & Norbury, P. (2024). Super volumes and KdV tau functions (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17272