Duality and Dynamical Supersymmetry Breaking in $Spin(10)$ with a Spinor

We study ${cal N}=1$ supersymmetric $Spin(10)$ chiral gauge theories with a single spinor representation and $N$ vector representations. We present a dual description in terms of an ${cal N}=1$ supersymmetric $SU(N-5)$ chiral gauge theory with a symmetric tensor, one fundamental and $N$ antifundamental representations. The $Spin(10)$ theory with $N=0$ breaks supersymmetry at strong coupling; we study how this arises at weak coupling in the dual theory, which is a spontaneously broken gauge theory. Also, we recover various known dualities, find new dual pairs and generate new examples of dynamical supersymmetry breaking.