Quantization of Flag Manifolds and their Supersymmetric Extensions

TL;DR

This paper develops fuzzy (quantized) versions of flag manifolds and their supersymmetric extensions, including Calabi-Yau supermanifolds, using Pluecker coordinates and coherent states.

Contribution

It introduces a novel construction of fuzzy flag supermanifolds and extends the Pluecker coordinate approach to supersymmetric cases.

Findings

Constructed fuzzy flag manifolds using operator and star product formalisms.

Extended the Pluecker coordinate description to supersymmetric flag manifolds.

Obtained fuzzy Calabi-Yau supermanifolds with potential applications in string theory.

Abstract

We first review the description of flag manifolds in terms of Pluecker coordinates and coherent states. Using this description, we construct fuzzy versions of the algebra of functions on these spaces in both operatorial and star product language. Our main focus is here on flag manifolds appearing in the double fibration underlying the most common twistor correspondences. After extending the Pluecker description to certain supersymmetric cases, we also obtain the appropriate deformed algebra of functions on a number of fuzzy flag supermanifolds. In particular, fuzzy versions of Calabi-Yau supermanifolds are found.