Vortex Filament in Three-manifold and the Duistermaat-Heckman Formula
Yukinori Yasui (Osaka City U.), Waichi Ogura (Osaka U.)
TL;DR
This paper explores the symplectic geometry of vortex filaments in curved three-manifolds, revealing an infinite sequence of conserved quantities and analyzing the Duistermaat-Heckman formula perturbatively.
Contribution
It introduces a novel analysis of vortex filaments in curved spaces and verifies the Duistermaat-Heckman formula up to 3-loop order in this context.
Findings
Existence of an infinite sequence of constants of motion in constant curvature cases
Perturbative verification of the Duistermaat-Heckman formula up to 3-loop order
Insights into symplectic structure of vortex filaments in curved three-manifolds
Abstract
Symplectic geometry of the vortex filament in a curved three-manifold is investigated. There appears an infinite sequence of constants of motion in involution in the case of constant curvature. The Duistermaat-Heckman formula is examined perturbatively for the classical partition function in our model and verified up to the 3-loop order.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.