Anti-selfdual Connections On The Quantum Projective Plane: Instantons

TL;DR

This paper investigates anti-selfdual instanton connections with instanton number 1 on the quantum projective plane, revealing a noncommutative family of solutions foliated by quantum projective planes.

Contribution

It introduces a new class of anti-selfdual connections on the quantum projective plane with reversed orientation, expanding understanding of noncommutative instantons.

Findings

Noncommutative family of solutions foliated by quantum projective planes

Existence of anti-selfdual connections with instanton number 1 in this setting

Orientation reversal affects the structure of instanton solutions

Abstract

We study one-instantons, that is anti-selfdual connections with instanton number 1, on the quantum projective plane with orientation which is reversed with respect to the usual one. The orientation is fixed by a suitable choice of a basis element for the rank 1 free bimodule of top forms. The noncommutative family of solutions is foliated, each non-singular leaves being isomorphic to the quantum projective plane itself.