Sinh Deformed Nakajima Operators

TL;DR

This paper introduces a new action of the 3D Heisenberg algebra on the equivariant K-theory of Hilbert schemes, linking algebraic geometry with supersymmetric gauge theories through Nakajima correspondences and instanton operators.

Contribution

It establishes a novel algebraic action on K-theory and connects it to physical instanton line operators via supersymmetric localization.

Findings

New Heisenberg algebra action on K-theory of Hilbert schemes

Identification of operators with instanton line operators in 6d SYM

Use of supersymmetric localization to relate geometry and physics

Abstract

We prove a novel action of the (three-dimensional) Heisenberg algebra on the equivariant K-theory of the Hilbert scheme of points on C2. These operators are defined via pushforwards and pullbacks via the Nakajima correspondences while tensoring the square roots of the canonical line bundles of the correspondences. We show, using supersymmetric localisation in 6d (1, 1) Super Yang-Mills compactified on a circle, that these operators correspond to instanton line operators wrapping the extra circle.