Related papers: Double ramification cycles and integrable hierarch…
We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomological field theory. Various checks are presented to support…
In a recent paper, giving an arbitrary homogeneous cohomological field theory (CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space local functionals that conjecturally gives a second Hamiltonian…
In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in [Bur15] using intersection theory of the double ramification cycle in the moduli space of stable…
We establish the Miura equivalence of two integrable systems associated to a semi-simple cohomological field theory: the double ramification hierarchy of Buryak and the Dubrovin-Zhang hierarchy. This equivalence was conjectured by Buryak…
The double ramification hierarchy is a new integrable hierarchy of hamiltonian PDEs introduced recently by the first author. It is associated to an arbitrary given cohomological field theory. In this paper we study the double ramification…
Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second…
In this paper we continue the study of the double ramification hierarchy of [Bur15]. After showing that the DR hierarchy satisfies tau-symmetry we define its partition function as the (logarithm of the) tau-function of the string solution…
In this paper we study various aspects of the double ramification (DR) hierarchy, introduced by the first author, and its quantization. We extend the notion of tau-symmetry to quantum integrable hierarchies and prove that the quantum DR…
Double ramification (DR) hierarchies associated to rank-$1$ F-CohFTs are important integrable perturbations of the Riemann--Hopf hierarchy. In this paper, we perform bihamiltonian tests for these DR hierarchies, and conjecture that the ones…
In [arXiv:2408.13806], two families of classical and quantum integrable hierarchies associated to arbitrary Cohomological Field Theories (CohFTs) were introduced: the meromorphic differential and twisted double ramification hierarchies. For…
In this paper we define a quantization of the Double Ramification Hierarchies of [Bur15b] and [BR14], using intersection numbers of the double ramification cycle, the full Chern class of the Hodge bundle and psi-classes with a given…
We introduce a new logarithmic structure on the moduli stack of stable curves, admitting logarithmic gluing maps. Using this we define cohomological field theories taking values in the logarithmic Chow cohomology ring, a refinement of the…
In this paper we compute explicitly the double ramification hierarchy and its quantization for the $D_4$ Dubrovin-Saito cohomological field theory obtained applying the Givental-Teleman reconstruction theorem to the $D_4$ Coxeter group…
We prove the so-called master relation in the tautological ring of the moduli space of curves that implies polynomial properties of the Dubrovin-Zhang hierarchies associated to different versions of cohomological field theories as well as…
We introduce the concept of integrable observables and propose them as alternatives to the standard Witten's psi classes (a.k.a. descendants in $2D$ quantum gravity) to be coupled with cohomological field theories and their generalisations.…
We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogeneous) flat F-manifold possesses a (homogeneous) integrable…
A super Hill operator with energy dependent potentials is proposed and the associated integrable hierarchy is constructed explicitly. It is shown that in the general case, the resulted hierarchy is multi-Hamiltonian system. The Miura type…
We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus $g$ with $n$ marked points. A large part of these relations has a surprisingly simple form: the…
The Dubrovin-Zhang hierarchy is a Hamiltonian infinite-dimensional integrable system associated to a semi-simple cohomological field theory or, alternatively, to a semi-simple Dubrovin-Frobenius manifold. Under an extra assumption of…
Starting from a so-called flat exact semisimple bihamiltonian structures of hydrodynamic type, we arrive at a Frobenius manifold structure and a tau structure for the associated principal hierarchy. We then classify the deformations of the…