Fierz identities in ten-dimensional superspace

Abstract

All SO(1,9)-irreducible bases composed of tensors and tensor–spinors, which span the whole space up to 16th-order polynomials in θ, θj ( j=1–16) being Majorana–Weyl spinors of SO(1,9), are explicitly constructed. Any superfield φ(xm,θ) in ten-dimensional superspace can be expanded by these bases, expansion coefficients being ordinary tensor and tensor–spinor fields. Then explicit formulas are given for φ(x,θ)Φ(x,θ) (Φ being another superfield) up to sixth order in θ in terms of ordinary fields, while those for (∂/∂θ̄)φ(x,θ) and Γmθ ∂mφ(x,θ) are given up to eighth order in θ.