Work

Towards quantum hierarchy for the Gromov–Witten theory of elliptic curves

Year: 2026

Type: article

Abstract: We construct the quantum double ramification (DR) hierarchy associated with the Gromov–Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the DR cycle, the Gromov–Witten classes of the elliptic curve, and the Hodge class , together with vanishing results for to produce a closed, modular expression for the resulting integrable hierarchy. It is the first explicit nontrivial example of a quantum integrable hierarchy from a cohomological field theory containing fermionic fields, which correspond to the odd classes in the cohomology of the elliptic curve.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70486

Authors: Paolo Rossi, Sergey Shadrin, Ishan Jaztar Singh

Institutions: University of Padua, University of Amsterdam

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Università degli Studi di Padova