In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of stable curves of any genus. These quadratic DR integrals are the main ingredients for the computation of the DR hierarchy associated to the infinite-dimensional partial cohomological field theory given by (Formula presented.), where (Formula presented.) is a parameter and (Formula presented.) is Hain's theta class, appearing in Hain's formula for the DR cycle on the moduli space of curves of compact type. This infinite rank DR hierarchy can be seen as a rank 1 integrable system in two space and one time dimensions. We prove that it coincides with a natural analogue of the Korteweg-de-Vries (KdV) hierarchy on a noncommutative Moyal torus.

Quadratic double ramification integrals and the noncommutative KdV hierarchy

Rossi P.
2021

Abstract

In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of stable curves of any genus. These quadratic DR integrals are the main ingredients for the computation of the DR hierarchy associated to the infinite-dimensional partial cohomological field theory given by (Formula presented.), where (Formula presented.) is a parameter and (Formula presented.) is Hain's theta class, appearing in Hain's formula for the DR cycle on the moduli space of curves of compact type. This infinite rank DR hierarchy can be seen as a rank 1 integrable system in two space and one time dimensions. We prove that it coincides with a natural analogue of the Korteweg-de-Vries (KdV) hierarchy on a noncommutative Moyal torus.
File in questo prodotto:
File Dimensione Formato  
quadraticDR-arxiv.pdf

accesso aperto

Tipologia: Preprint (submitted version)
Licenza: Accesso gratuito
Dimensione 206.98 kB
Formato Adobe PDF
206.98 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3380701
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 4
social impact