TY - JOUR

T1 - Quadratic double ramification integrals and the noncommutative KdV hierarchy

AU - Buryak, Alexandr

AU - Rossi, Paolo

N1 - Publisher Copyright: © 2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/6

Y1 - 2021/6

N2 - 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.

AB - 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.

KW - 14H10

KW - 37K10 (primary)

UR - http://www.scopus.com/inward/record.url?scp=85100190820&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=44968859

U2 - 10.1112/blms.12464

DO - 10.1112/blms.12464

M3 - Article

AN - SCOPUS:85100190820

VL - 53

SP - 843

EP - 854

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 3

ER -