2023/09/21 by Guo, Shuai, Ji, Ce, Zhang, Qingsheng · 1 citation
#14J33 #14N35 #37K10 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2309.12271
We propose a generalization of the Witten conjecture, which connects a descendent enumerative theory with a specific reduction of KP integrable hierarchy. Our conjecture is realized by two parts: Part I (Geometry) establishes a correspondence between the geometric descendent potential (apart from ancestors) and the topological recursion of specific spectral curve data (Σ, x,y); Part II (Integrability) claims that the TR descendent potential, defined at the boundary points of the spectral curve (where dx has poles), is a tau-function of a certain reduction of the multi-component KP hierarchy. In this paper, we show the geometric part of the conjecture for any formal descendent theory by using a generalized Laplace transform. Subsequently, we prove the integrability conjecture for the one-boundary cases. As applications, we generalize and prove the rKdV integrability of negative r-spin theory conjectured by Chidambaram, Garcia-Failde and Giacchetto. We also show the KdV integrability of the total descendent potential associated with the Hurwitz space M1,1, whose Frobenius manifold was initially introduced by Dubrovin.