A HIERARCHY OF GAUGED GRASSMANIAN MODELS IN $4p$ DIMENSIONS WITH SELF-DUAL INSTANTONS

TL;DR

This paper introduces a hierarchy of gauged Grassmanian models in 4p dimensions, characterized by self-duality equations that simplify to coupled ODEs under spherical symmetry, advancing understanding of higher-dimensional gauge theories.

Contribution

It develops a new hierarchy of models in 4p dimensions with self-duality equations, extending the framework of gauge theories in higher dimensions.

Findings

Models are minimized by self-duality equations.

Self-duality equations reduce to coupled ODEs under spherical symmetry.

Provides a systematic hierarchy for gauged Grassmanian models.

Abstract

We present a hierarchy of gauged Grassmanian models in $4p$ dimensions, where the gauge field takes its values in the $2^{2p- 1}\times 2^{2p-1}$ chiral representation of SO(4p). The actions of all these models are absolutely minimised by a hierarchy of self-duality equations, all of which reduce to a single pair of coupled ordinary differential equations when subjected to $4p$ dimensional spherical symmetry.