Generalized nonlinear sigma models on symmetric spaces

We point out that the nonlinear sigma models on symmetric spaces as considered by Eichenherr and Forger can be generalized to include a larger class of models possessing dual symmetry. The well-known axially symmetric gravitational vacuum and electrovac problems as well as the axially symmetric Kaluza-Klein dyons fall into this class.     

On classicalization in nonlinear sigma models

We consider the phenomenon of classicalization in nonlinear sigma models with both positive and negative target space curvature and with any number of derivatives. We find that the theories with only two derivatives exhibit a weak form of classicalization, and that the quantitative results depend on the sign of the curvature. Nonlinear sigma models with higher derivatives show a strong form of the phenomenon which is independent of the sign of curvature. We argue that weak classicalization may actually be equivalent to asymptotic safety, whereas strong classicalization seems to be a genuinely different phenomenon. We also discuss possible ambiguities in the definition of the classical limit.     

Supersymmetric nonlinear sigma models constrained on non-compact manifold

A detailed analysis by 1/n expansion is presented of supersymmetric nonlinear sigma models in two dimensions withU(n) symmetry in which the scalar fields are constrained on a non-compact manifold. The theories are ultraviolet finite. In the massless version of the models no mass scale is generated and gauge bosons fail to get dynamics while this is possible provided the theory contains a mass scale. The effects of introduction of the “Ø-term” into supersymmetric theories are also discussed. In particular, it is argued that supersymmetry is broken by the Ø-term only in finite supersymmetric theories. Finally, a singular behavior in the massless limit in these models is pointed out.     

Hyperbolic complex numbers and nonlinear sigma models

We show that the hyperbolic complex numbers or double numbers can be used to generate solutions of two-dimensional Minkowskian sigma models with values on noncompact manifolds.     

Classical solutions of higher-dimensional nonlinear sigma models on spheres

We construct several classical solutions of higher-dimensional nonlinear sigma models on spheres. These solutions are characterized by typical topological maps, in particular, four famous Hopf maps and the universal maps of theK-theory.Dedicated to the late Professor Shichiro Oka.     

Exact classical solutions of nonlinear sigma models on supermanifolds

We study two-dimensional nonlinear sigma models with target spaces being the complex super-Grassmannian manifolds, that is, coset supermanifolds G(m,p|n,q)≅U(m|n)/[U(p|q)⊗U(m−p|n−q)]$G(m,p|n,q)\cong U(m|n)/[U(p|q)\otimes U(m-p|n-q)]$ for 0?p?m$0?p?m$, 0?q?n$0?q?n$ and 1?p+q$1?p+q$. The projective superspace CPm−1|n${\mathbf{CP}}^{m-1|n}$ is a special case of p=1$p=1$, q=0$q=0$. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmonic maps) are constructed explicitly and elementarily in terms of Gramm–Schmidt orthonormalisation procedure starting from holomorphic bosonic and fermionic supervector input functions. The construction is a generalisation of the non-super-case published more than twenty years ago by one of the present authors.     

Current conservation and parallelism in nonlinear sigma models

We examine the consequences of a restrictive current conservation condition, which figures in the bosonization of certain free fermion theories, when applied to a general bosonic nonlinear sigma model in two dimensions. The condition is shown to lead directly to the existence of parallelizing Killing vector fields on the internal manifold. The current algebra is checked to have the expected Kac-Moody form.     

Higher local conservation laws for nonlinear sigma models on symmetric spaces

We show that for the classical two-dimensional nonlinear -model on a Riemannian symmetric space of dimensionm and rankp, there existp independent series of higher local conservation laws, and we reduce the field equations of the model to a system of nonlinear partial differential equations possessing an associated Lax pair and involvingm+p independent variables.Dedicated to the Memory of our Colleague and Friend Jorge André SwiecaWork partially done under DFG contract Schr 4/5     

Supersymmetric topological terms in D = 3 nonlinear sigma models

We discuss generalized Wess-Zumino-Witten terms in supersymmetric nonlinear sigma models on three-dimensional spacetime, and give a natural N = 2 supersymmetric term for any Kähler manifold. We show that the coefficient is not quantized if isometries of the manifold are not gauged. The relation between generalized Wess-Zumino-Witten terms in different spacetime dimensions is discussed, and some useful superspace methods are introduced.     

Anomaly constraints on supersymmetric effective lagrangians

In this paper we set constraints on the possible effective-lagrangian representations of supersymmetric gauge theories with spontaneously broken chiral flavor symmetries, by finding the conditions under which a Wess-Zumino term to represent the anomalous interactions can be constructed. We find that effective lagrangians for such theories are possible only for nonlinear sigma models defined on noncompact manifolds, and demonstrate the realization of this result in supersymmetric QCD. We also consider the Wess-Zumino term in the nonlinear realization of broken supersymmetry.     

Massive nonlinear sigma models and BPS domain walls in harmonic superspace

Four-dimensional massive nonlinear sigma models and BPS wall solutions are studied in the off-shell harmonic superspace approach in which supersymmetry is manifest. The general nonlinear sigma model can be described by an analytic harmonic potential which is the hyper-Kähler analog of the Kähler potential in theory. We examine the massive nonlinear sigma model with multi-center four-dimensional target hyper-Kähler metrics and derive the corresponding BPS equation. We study in some detail two particular cases with the Taub-NUT and double Taub-NUT metrics. The latter embodies, as its two separate limits, both Taub-NUT and Eguchi–Hanson metrics. We find that domain wall solutions exist only in the double Taub-NUT case including its Eguchi–Hanson limit.