The effective potential in extended supersymmetric non-linear sigma models

It is proved that for a certain class of off-shell formulations the effective potential is either renormalizable, or extended supersymmetry is broken by the effects of renormalization. Examples of the latter are given and possibilities for the former are discussed. Explicit two loop calculations support the general results.     

Non-perturbative effects in supersymmetric sigma models

A scheme for taking account of crucial non-perturbative effects in a quantum field theory ahead of developing perturbation series for it is extended here from bosonic to supersymmetric sigma models in two dimensions. The scheme writes field products in the lagrangian in terms of suitably defined normal ordered products and VEVs of field products. The exact values of the latter can be inferred directly from the symmetry and supersymmetry Ward identities of the theory, so that a lagrangian with scale breaking effects explicitly treated, is available for use in perturbation theory. The supersymmetric sigma model on the manifold S^N is used to illustrate many aspects of the scheme.     

Coupling the gauge-invariant supersymmetric non-linear sigma model to supergravity

The gauge-invariant supersymmetric non-linear sigma model is coupled to N = 1 supergravity. The results are expressed in the language of Kahler geometry. They lead to a deeper understanding of the connections between supergravity, R-invariance and the Fayet-Iliopoulos D-term. They also provide a foundation for phenomenological studies of supergravity theories.     

Finiteness of N = 4 supersymmetric sigma models

The two-dimensional supersymmetric K3 σ-model is not renormalized in all orders of perturbation theory.     

Current algebra of classical non-linear sigma models

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether currentj associated with the global symmetry of the theory, a composite scalar fieldj, the algebra closes under Poisson brackets.Address after September 1, 1991: Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge MA 02138, USA. Supported by the Studienstiftung des Deutschen Volkes     

Classical integrability of two-dimensional non-linear sigma models

The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature relation. Some new integrable two-dimensional sigma models are then presented.     

The Lie-Poisson structure of integrable classical non-linear sigma models

The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into ther-s-matrix formalism for non-ultralocal integrable models first discussed by Maillet. The matricesr ands are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrixc. It is proposed that all these Poisson brackets taken together are, representation conditions for a new kind of algebra which, for this class of models, replaces the classical Yang-Baxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed.Suported by the Deutsche Forschungsgemeinschaft, Contract No. Ro 864/1-1Supported by the Studienstiftung des Deutschen Volkes     

On the dual symmetry of the non-linear sigma models

We analyze the dual symmetry which is reponsible for the existence of infinitely many conserved non-local charges in the classical two-dimensional non-linear σ models. For compact global symmetry groups, we prove that the σ model has the dual symmetry if and only if the field takes values in a symmetric space.     

The algebra of non-local charges in non-linear sigma models

We obtain the exact classical algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry groupO(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, now containing a calculable correction of order one unit lower. The relation with Yangians and the role of the results in the context of Lie-Poisson algebras are also discussed.Supported by FAPESP.Supported by CNPq.Supported by CNPq     

Beta functions and central charge of supersymmetric sigma models with torsion

We present a method for the computation of the renormalization group β-functions and the central charge in two-dimensional supersymmetric sigma models in a gravitational background. The two-loops results are exhibited. We use the Pauli-Villars regularization which preserves supersymmetry and permits an unambiguous treatment of the model with torsion. The central charge we derive for a general manifold is in agreement with the expression found on group manifolds.     

On the geometry of classically integrable two-dimensional non-linear sigma models

A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.     

(8,0) Locally supersymmetric sigma models with conformal invariance in two dimensions

The (8,0) conformal supergravity, and an action which describes its coupling to an arbitrary number of (8,0) scalar multiplets are constructed. The 64+64 components of the conformal supermultiplet occur as Lagrange multipliers which lead to differential and algebraic constraints on the fields of the scalar multiplets. Solving the algebraic constraints yields an (8,0) locally supersymmetric sigma model based on the manifold SO(8 + n,m)/SO(8)×SO(n,m), where n,m ⩾ 0.     

Spontaneous breakdown and finiteness of supersymmetric theories in two dimensions

Using a single scalar superfield we construct the two dimensional version of the four dimensional Wess-Zumino model and examine its renormalization properties. In the context of this model and in the tree approximation we find that supersymmetry can be spontaneously broken with the appearance of a massless fermion. This solution is then shown to be dynamically unstable at the one-loop level. Finally we use supersymmetry to construct two dimensional theories for which all IPI vertices are finite.     

Homogeneous Kähler manifolds: Paving the way towards new supersymmetric sigma models

Homogeneous Kähler manifolds give rise to a broad class of supersymmetric sigma models containing, as a rather special subclass, the more familiar supersymmetric sigma models based on Hermitian symmetric spaces. In this article, all homogeneous Kähler manifolds with semisimple symmetry groupG are constructed, and are classified in terms of Dynkin diagrams. Explicit expressions for the complex structure and the Kähler structure are given in terms of the Lie algebra g ofG. It is shown that for compactG, one can always find an Einstein-Kähler structure, which is unique up to a constant multiple and for which the Kähler potential takes a simple form.On leave of absence from Fakultät für Physik der Universität Freiburg, FRG