Integrable systems of finite type from F-cohomological field theories without unit (Q6072343)

The topic of paper belongs to a contemporary mathematical field of research linking integrable systems and moduli spaces of algebraic curves. The paper is based on the notion of double ramification hierarchy introduced by one of the authors in [\textit{A. Buryak}, Commun. Math. Phys. 336, No. 3, 1085--1107 (2015; Zbl 1329.14103)], and the notion of so-called Frobenius cohomological field theory introduced in [\textit{A. Arsie} et al., Commun. Math. Phys. 388, No. 1, 291--328 (2021; Zbl 1489.37083)]. One can relate a double ramification hierarchy to an arbitrary Frobenius cohomological field theory. Generally speaking, the equations of such an integrable hierarchy admit infinite expansions of dispersion parameter. In the current paper, the authors describe a new family of Frobenius cohomological field theories without unit whose double ramification hierarchy consists of equations having finite expansions of the dispersion parameter. In the simplest case, the primary flows of that hierarchy are explicitly derived. The paper will mainly be of interest for algebraic geometers with certain expertise in integrable systems.