Coupling the Supersymmetric 210 Vector Multiplet to Matter in SO(10)

TL;DR

This paper analyzes the couplings of the 210-dimensional SO(10) vector multiplet to matter fields, providing detailed decomposition and interaction structures, with potential applications in effective theories involving condensates.

Contribution

It presents a detailed decomposition of the 210 vector multiplet couplings to matter in SO(10), including nonlinear Lagrangian derivation and comprehensive coupling computations.

Findings

Decomposition of vector couplings into SU(5)×U(1) components.

Derivation of nonlinear sigma model type Lagrangian.

Complete computation of lowest order couplings involving 16 spinors.

Abstract

An analysis of the couplings of the 210 dimensional SO(10) vector multiplet to matter is given. Specifically we give an $SU(5)\times U(1)$ decomposition of the vector couplings $\bar{16}_{\pm}-16_{\pm}-210$, where $16_{\pm}$ is the semispinor of SO(10) chirality ${\pm}$, using a recently derived basic theorem. The analysis is carried out using the Wess-Zumino gauge. However, we also consider the more general situation where all components of the vector multiplet enter in the couplings with the chiral fields. Here elimination of the auxiliary fields leads to a sigma model type nonlinear Lagrangian. Interactions of the type analysed here may find applications in effective theories with the 210 vector arising as a condensate. The analysis presented here completes the explicit computation of all lowest order couplings involving the $16_{\pm}$ of spinors with Higgs and vectors multiplets using the basic theorem.