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

TL;DR

This paper develops a method for constructing anomaly-free supersymmetric sigma-models on coset spaces like SO(2N)/U(N), analyzing their global properties, vacuum structure, and conditions for consistency and physical viability.

Contribution

It introduces a procedure for coupling gauge and matter superfields to sigma-models on symmetric Kaehler cosets, including the construction of Killing potentials and analysis of anomaly cancellation.

Findings

Certain models can incorporate matter from spinorial representations.

The fully gauged SO(10)/U(5) model is singular in the vacuum.

Gauging only subgroups like SU(5)xU(1) yields well-behaved theories.

Abstract

This paper discusses a procedure for the consistent coupling of gauge- and matter superfields to supersymmetric sigma-models on symmetric coset spaces of Kaehler type. We exhibit the finite isometry transformations and the corresponding Kaehler 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 be singular, as the kinetic terms of the quasi-Goldstone fermions vanish in the vacuum. Gauging only the linear isometry group SU(5)xU(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.