# 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…

## 20 Citations

### Integrable Systems of Double Ramification Type

- MathematicsInternational Mathematics Research Notices
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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…

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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…

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### The quantum Witten–Kontsevich series and one-part double Hurwitz numbers

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We study the quantum Witten-Kontsevich series introduced by Buryak, Dubrovin, Guere and Rossi in \cite{buryak2016integrable} as the logarithm of a quantum tau function for the quantum KdV hierarchy.…

### INTEGRABLE SYSTEMS AND MODULI SPACES OF CURVES

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- 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…

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