Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter

TL;DR

This paper develops a Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter, enabling topologically nontrivial configurations and chiral fermion realization in matrix models of superstring theory.

Contribution

It formulates a Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter, establishing an index theorem applicable to monopole configurations.

Findings

Index theorem satisfied for adjoint matter

Applicable to topologically nontrivial configurations like monopoles

Provides a basis for realizing chiral fermions in matrix models

Abstract

We formulate a Ginsparg-Wilson relation on a fuzzy 2-sphere for matter in the adjoint representation of the gauge group. Because of the Ginsparg-Wilson relation, an index theorem is satisfied. Our formulation is applicable to topologically nontrivial configurations as monopoles. It gives a solid basis for obtaining chiral fermions, which are an important ingredient of the standard model, from matrix model formulations of the superstring theory, such as the IIB matrix model, by considering topological configurations in the extra dimensions. We finally discuss whether this mechanism really works.