Spinors and theta deformations

Harmonic spinors and local deformations of the metric

Let (M, g) be a compact Riemannian spin manifold. The AtiyahSinger index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this bound can be attained by changing the Riemannian metric g on an arbitrarily small open set.

SPINORS and

Spinors and Octonions

Octonions are introduced through some spin representations. The groups G2, F4 and the E series appear in a natural manner; one way to understand octonions is as the “second coming” of the reals, but with the spinors instead of vectors. Some physical applications in M and F -theory as putative “theories of everything” are suggested. 1 The Seven Sphere . Consider the real, complex and quaternion ...

Spinors and Supersymmetry

Abstract. In this paper, we survey the nature of spinors and supersymmetry (SUSY) in various types of spaces. We treat two distinct types of spaces: flat spaces and spaces of constant (non-zero) curvature. The flat spaces we consider are either three or four dimensional of signatures 3 + 1, 4 + 0, 2 + 2 and 3 + 0. In each of these cases, SUSY generators anti-commute to yield the generators of t...

Delocalised Spinors

Solutions to the four-dimensional Euclidean Weyl equation in the background of a general JNR N -instanton are known to be normalisable and regular throughout four-space. We show that these solutions are asymptotically given by a linear combination of simple singular solutions to the free Weyl equation, which can be interpreted as localised spinors. The ‘spinorial’ data parameterising the asympt...