Jürgen Fuchs

More on the super WZW theory

Abstract The super WZW theory is analyzed further. The quantum equivalence to a bosonic WZW theory supplemented by free fermions is proven rigorously, and implications of this equivalence are investigated both in the Neveu-Schwarz and in the Ramond sector of the theory.

The computation of the operator algebra in non-diagonal conformal field theories

The computation of the operator algebra in conformal field theories with Feigin-Fuks type correlation functions is described. The special features of non-diagonal theories are pointed out. Detailed formulae are provided for the {ital c}{lt}1 minimal series and for {ital A}{sub 1} WZW theories. As examples, the operator product coefficients for the {bold E}{sub 6}, {bold E}{sub 7}, and {bold D}{sub {ital l}} type {ital A}{sub 1} WZW theories are calculated. {copyright} 1989 Academic Press, Inc.

String Field Equations and the Dual S Matrix From the Exact Renormalization Group

Abstract We investigate explicitly the variation, with respect to the Liouville mode α, of the Polyakov path integral corresponding to the closed bosonic string, including sources for all massless and massive string modes. Global conformal invariance is seen to imply a set of equations of motion for these sources, which we derive in closed form. The consideration of non-trivial backgrounds requires one to carry out a renormalization procedure, which generates renormalization type equations valid away from the conformal point. In the trivial vacuum the equations of motion involve just a bilinear interaction term which is closely related to operator product coefficients. The iterative solution to these equations allows us to construct the dual S-matrix.

Level-Rank Duality of WZW Theories and Isomorphisms of N = 2 Coset Models

Abstract Mappings between certain infinite series of N = 2 superconformal coset models are constructed. They make use of level-rank dualities for B , C , and D type WZW theories, which are described in some detail. The WZW level-rank dualities do not constitute isomorphisms of the theories; for example, for B and D type WZW theories only simple current orbits rather than individual primary fields are mapped onto each other. Nevertheless they lead to level-rank dualities of N = 2 coset models that preserve the conformal field theory properties in such a manner that the coset models related by duality are expected to be, in fact, isomorphic as conformal field theories; in particular, the representation of the modular group on the characters and the ground states of the Ramond sector are shown to coincide. The construction also gives some further insight into the nature of the resolution of field identification fixed points of coset theories.

The heterotic σ-model with background gauge fields

Abstract We develop methods for simplifying considerably the computation of β-functions for the heterotic σ-model in the presence of background gauge fields. These methods are used to obtain three-loop results. Up to the overall normalization of the O(α- ′2 ) contribution, the β-functions are on-shell equivalent to the equations of motion derived from an effective action which has been obtained previously in the string S -matrix approach. Our results shed, however, new light on the off-shell relation between these field equations and the β-functions. It is also shown that, to all orders in α′, the net effect of gauge anomalies is the addition of a Chern-Simons term to the torsion.

Remarks on supersymmetric quantum mechanics at finite temperature

Abstract We discuss the finite temperature behavior of supersymmetric quantum mechanics. We give some general results on energy eigenvalues and eigenstates and discuss their implications on susy breaking. For some models we derive exact solutions. In addition we remark on peculiarities occurring if the formalism of thermo field dynamics is used in supersymmetric theories.

Thermal and superthermal properties of supersymmetric field theories

Abstract We discuss the finite-temperature behaviour of supersymmetric field theories. We show that their “superthermal” properties which concern the question of susy breaking at finite temperature and their thermal properties must be considered separately. Susy breaking is determined by the so-called superthermal ensemble, whereas thermodynamical properties follow from the conventional thermal ensemble, leading to the usual statistics for the bosonic and fermionic components of a superfield. We show that superspace techniques can be used in a straightforward way only for superthermal Green functions but not for thermal ones. We also discuss the possibility of finite-temperature susy restoration and the implications of Goldstones theorem at finite temperature.

Conformal embeddings and hidden symmetries of free fermion theories

It is shown that the conformal field theory of free complex fermions transforming in the (anti)symmetric tensor representation R of u(N) is characterized by a nontrivial operator algebra. However, this theory can be naturally embedded into the theory of free Dirac fermions in the defining representation of u(dimR); the latter theory corresponds to an operator algebra which is trivial in the sense that e.g. φ×φ+ = 1. We argue that these observations can be generalized to any system of free fermions possessing an energy-momentum tensor of the Sugawara form. As a consequence, there exist no further cases where a free fermion theory is quantum equivalent to a WZW theory, besides the ones already well known (i.e. those based on the current algebras so(N) and u(N) with unit central charge).

The connections between Wess-Zumino-Witten models and free field theories

Abstract The relations between Wess-Zumino-Witten models and free field theories are reviewed. In particular the possibility of quantum equivalence between these two types of conformal field theories is investigated. Supersymmetric Wess-Zumino-Witten models are also discussed.

Nonrenormalizable field theories at finite temperature

We comment on the effects of finite temperature in two purely fermionic theories. While in the Nambu-Jona-Lasinio model a second order phase transition takes place, we find no phase transition in a model of composite gauge bosons.