# Double Ramification Cycles and Quantum Integrable Systems

@article{Buryak2015DoubleRC, title={Double Ramification Cycles and Quantum Integrable Systems}, author={Alexandr Buryak and Paolo Rossi}, journal={Letters in Mathematical Physics}, year={2015}, volume={106}, pages={289-317} }

In this paper, we define a quantization of the Double Ramification Hierarchies of Buryak (Commun Math Phys 336:1085–1107, 2015) and Buryak and Rossi (Commun Math Phys, 2014), using intersection numbers of the double ramification cycle, the full Chern class of the Hodge bundle and psi-classes with a given cohomological field theory. We provide effective recursion formulae which determine the full quantum hierarchy starting from just one Hamiltonian, the one associated with the first descendant… Expand

#### 18 Citations

Integrable Systems of Double Ramification Type

- Mathematics, Physics
- International Mathematics Research Notices
- 2019

In this paper we study various aspects of the double ramification (DR) hierarchy, introduced by the 1st author, and its quantization. We extend the notion of tau-symmetry to quantum integrable… Expand

Tau-Structure for the Double Ramification Hierarchies

- Mathematics, Physics
- 2016

In this paper we continue the study of the double ramification hierarchy of Buryak (Commun Math Phys 336(3):1085–1107, 2015). After showing that the DR hierarchy satisfies tau-symmetry we define its… Expand

D ec 2 01 8 TAU-STRUCTURE FOR THE DOUBLE RAMIFICATION HIERARCHIES

- 2018

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… Expand

Quantum D4 Drinfeld–Sokolov hierarchy and quantum singularity theory

- Physics, Mathematics
- Journal of Geometry and Physics
- 2019

Abstract 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… Expand

Integrability, Quantization and Moduli Spaces of Curves

- Physics, Mathematics
- 2017

This paper has the purpose of presenting in an organic way a new approach to integrable (1+1)-dimensional field systems and their systematic quantization emerging from intersection theory of the… Expand

Towards a description of the double ramification hierarchy for Witten's $r$-spin class

- Mathematics, Physics
- 2015

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… Expand

INTEGRABLE SYSTEMS AND MODULI SPACES OF CURVES

- Mathematics
- 2016

This document has the purpose of presenting in an organic way my research on integrable systems originating from the geometry of moduli spaces of curves, with applications to Gromov-Witten theory and… Expand

Quantum hydrodynamics from large-n supersymmetric gauge theories

- Physics, Mathematics
- 2015

We study the connection between periodic finite-difference Intermediate Long Wave ($$\Delta \hbox {ILW}$$ΔILW) hydrodynamical systems and integrable many-body models of Calogero and Ruijsenaars-type.… Expand

Flat F-Manifolds, F-CohFTs, and Integrable Hierarchies

- Physics, Mathematics
- 2020

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… Expand

DR/DZ equivalence conjecture and tautological relations

- Mathematics, Physics
- 2017

In this paper we present a family of conjectural relations in the tautological ring of the moduli spaces of stable curves which implies the strong double ramification/Dubrovin-Zhang equivalence… Expand

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