Solutions of the loop equations of a class of generalized Frobenius manifolds
Mathematical Physics
2024-08-22 v2 Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We prove the existence and uniqueness of solution of the loop equation associated with a semisimple generalized Frobenius manifold with non-flat unity, and show, for a particular example of one dimensional generalized Frobenius manifold, that the deformation of the Principal Hierarchy induced by the solution of the loop equation is the extended q-deformed KdV hierarchy.
Keywords
Cite
@article{arxiv.2402.00373,
title = {Solutions of the loop equations of a class of generalized Frobenius manifolds},
author = {Si-Qi Liu and Haonan Qu and Yuewei Wang and Youjin Zhang},
journal= {arXiv preprint arXiv:2402.00373},
year = {2024}
}
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41 pages