Massless solutions for families of spinors for the toy model in $d=(1+5)$

TL;DR

This paper presents massless solutions for coupled spinor equations on a curved 2D surface, analyzing their normalizability and interactions with specific spin connection fields in a six-dimensional model.

Contribution

It provides explicit massless solutions for spinor families in a 6D toy model with curved geometry and specific spin connection interactions, advancing understanding of spinor behavior in higher dimensions.

Findings

Massless solutions are explicitly constructed.

Normalizability conditions are discussed.

Interactions with two types of spin connection fields are analyzed.

Abstract

Massless solutions for four coupled first order differential equations for functions representing families of spinors on the infinite disc curled into an almost $S^2$ are presented and normalizability conditions discussed. Spinors interact with two kinds of spin connection fields of particular coordinate dependence. This is the solution of equations of motion used in "Families of spinors in $d=(1+5)$ with zweibein and two kinds of spin connection fields on an almost $S^2$".