BKP and CKP hierarchies via orbifold Saito theory

TL;DR

This paper demonstrates that the BKP and CKP integrable hierarchies can be constructed from Dubrovin-Frobenius manifolds using orbifold Saito theory, extending previous methods that relied on classical Saito theory.

Contribution

It introduces a novel construction of BKP and CKP hierarchies via orbifold Saito theory applied to Dubrovin-Frobenius manifolds, broadening the scope of integrable hierarchy generation.

Findings

BKP and CKP hierarchies can be derived from orbifold Saito theory.

The construction extends existing methods based on classical Saito theory.

New connections between orbifold singularities and integrable systems are established.

Abstract

Semisimple Dubrovin-Frobenius manifolds can be used to construct integrable hierarchies, following the work of Dubrovin-Zhang and Buryak. Examples of such hierarchies include the Kac-Wakimoto hierarchies, the KP hierarchy, among others. In all these examples, the Saito theory of isolated singularities played a crucial role. In this note, we show that the BKP and CKP hierarchies can likewise be constructed from Dubrovin-Frobenius manifolds. This new construction, however, utilizes the orbifold version of Saito theory for isolated singularities endowed with a symmetry group.