Construction and analysis of anomaly-free supersymmetric SO(2N)/U(N) σ-models

This paper discusses a procedure for the consistent coupling of gauge- and matter superfields to supersymmetric sigma-models on symmetric coset spaces of Kähler type. We exhibit the finite isometry transformations and the corresponding Kähler transformations. These lead to the construction of a generalized type of Killing potentials. In certain cases a charge quantization condition needs to be imposed to guarantee the global existence of a line bundle on a coset space. The results are applied to the explicit construction of sigma-models on cosets SO(2N)/U(N). Only a finite number of these models can consistently incorporate matter in representations descending from the spinorial representations of SO(2N). We investigate in detail some aspects of the vacuum structure of the gauged SO(10)/U(5) theory, with surprising results: the fully gauged minimal anomaly-free model is shown to be singular, as the kinetic terms of the quasi-Goldstone fermions vanish in the vacuum. Gauging only the linear isometry group SU(5)×U(1), or one of its subgroups, can give a physically well-behaved theory. With gauged U(1) this requires the Fayet–Iliopoulos term to take values in a specific limited range.