Complete Cubic and Quartic Couplings of 16 and $\bar {16}$ in SO(10) Unification

TL;DR

This paper analytically determines all cubic superpotential couplings involving 16 and 16 in SO(10) unification, including previously uncomputed tensor representations, and discusses their implications for model building.

Contribution

It provides a complete analytic calculation of SO(10) invariant cubic couplings involving 16, 16, and tensor representations, extending previous work and analyzing large tensor effects.

Findings

Computed couplings involving 1, 45, 210 tensor representations.

Analyzed vector couplings 16 with these tensors.

Discussed implications for model building and large tensor roles.

Abstract

A recently derived basic theorem on the decomposition of SO(2N) vertices is used to obtain a complete analytic determination of all SO(10) invariant cubic superpotential couplings involving $16_{\pm}$ semispinors of SO(10) chirality $\pm$ and tensor representations. In addition to the superpotential couplings computed previously using the basic theorem involving the 10, 120 and $\bar{126}$ tensor representations we compute here couplings involving the 1, 45 and 210 dimensional tensor representations, i.e., we compute the $\bar{16}_{\mp}16_{\pm}1$,$\bar{16}_{\mp}16_{\pm}45$ and $\bar{16}_{\mp}16_{\pm}210$ Higgs couplings in the superpotential. A complete determination of dimension five operators in the superpotential arising from the mediation of the 1, 45 and 210 dimensional representations is also given. The vector couplings $\bar{16}_{\pm}16_{\pm}1$, $\bar{16}_{\pm}16_{\pm}45$ and $\bar{16}_{\pm}16_{\pm}210$ are also analyzed. The role of large tensor representations and the possible application of results derived here in model building are discussed.