Bifundamental Fuzzy 2-Sphere and Fuzzy Killing Spinors

TL;DR

This paper introduces a bifundamental fuzzy 2-sphere model, relating it to fuzzy Killing spinors and demonstrating its equivalence to the traditional fuzzy sphere, with implications for field theory and compactification.

Contribution

It presents a novel bifundamental construction of the fuzzy 2-sphere and explores its relation to fuzzy Killing spinors, expanding the mathematical and physical understanding of fuzzy geometries.

Findings

Bifundamental fuzzy sphere is equivalent to the usual fuzzy sphere.

Mathematical details of the bifundamental fuzzy sphere are elucidated.

Impacts on field twisting and compactification are analyzed.

Abstract

We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint) fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional) field theory.