Matter coupling and anomaly cancellation in supersymmetric σ-models

Abstract

Generalized matter couplings to four-dimensional supersymmetric sigma models on general Kähler manifolds are presented, preserving all holomorphic symmetries. Our generalization allows assignment of arbitrary U (1) charges to additional matter fermions, in all representations of (the holomorphic part of) the isometry group. This can be used to eliminate unwanted γ 5 anomalies, in particular for the U(1) symmetry arising from the complex structure of the target space. A consistent gauging of this isometry group, or any of its subgroups, then becomes possible. When gauged in the presence of a chiral scalar multiplet, the U(1) symmetry is broken spontaneously, generating a mass for the U(1) vector multiplet via the supersymmetric Higgs effect. As an example we discuss the case of the homogeneous coset space E 6 /SO(10) × U (1).

Coupling Supersymmetric Nonlinear Sigma Models to Supergravity

“…Nibbelink and van Holten 7) have proposed a method of making the Kähler potential G-invariant to circumvent the above problem. * ) They have added matter fields S i and assigned a U (1) charge q i to them such that the superpotential W (S) carries charge three.…”

Chaotic inflation from nonlinear sigma models in supergravity

“…Such functions have no effect in global supersymmetry when integrated over all of superspace, but in local supersymmetry they do not disappear. Here, too, there are several solutions which have been studied in the past [7,8] (see also [9] and [10] for earlier work). Generally one must consider a noncompact NLSM, G /H, which can be coupled to supergravity.…”

Singular supersymmetric σ-models

“…Supersymmetric pure σ-models on cosets, including among others the grassmannian models on SU(n + m)/[SU(n) × SU(m) × U(1)] and the models on manifolds SO(2n)/U(n), are known to be anomalous [4,5,6], since they incorporate chiral fermions in non-trivial representations of the holonomy group. These anomalies can be removed by coupling additional chiral superfields carrying specific line-bundle representations of the group G [7,8]. In a study of anomaly-free extended supersymmetric σ-models on coset manifolds of the type SO(2n)/U(n), it was found that the resulting field metric can develop singularities in the form of zero-modes, and therefore may not be positive definite [3].…”