Duality of N=1 Supersymmetric SO(10) Gauge Theory with Matter in the Spinorial Representation

TL;DR

This paper explores a duality in N=1 supersymmetric SO(10) gauge theory with matter in the spinorial representation, revealing new dual descriptions for specific flavor numbers and connecting to known chiral-vector dualities.

Contribution

It demonstrates a novel duality between SO(10) and SU(N_f-5) gauge theories with specific matter content for N_f=7,8, extending the understanding of supersymmetric gauge theory dualities.

Findings

Dual descriptions for N_f=7,8 in SO(10) gauge theory.

Different matter content for N_f=7 and N_f=8 cases.

Connection to Pouliot's duality between chiral and vector gauge theories.

Abstract

We study $N=1$ supersymmetric $SO(10)$ gauge theory with a field in the spinorial representaition and $N_f$ ($\leq8$) fields in the defining representation. It is shown that this theory for $N_f=7,8$ has a dual description, which is $N=1$ supersymmetric $SU(N_f-5)$ gauge theory. Its matter content for $N_f=7$ is different {}from the one for $N_f=8$; for $N_f=7$, it contains $8$ fields in the anti-fundamental representation. For $N_f=8$, a rank-$2$ symmetric tensor and one field in the fundamental representation appears in addition to them. This duality connects along the flat direction to the duality between chiral and vector gauge theory found by Pouliot.