Conformal field theories in six-dimensional twistor space

This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space–time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the six-dimensional case in which twistor space is the 6-quadric Q$Q$ in CP⁷${\mathbb{C}\mathbb{P}}^7$ with a view to applications to the self-dual (0,2)$(0,2)$-theory. We show how spinor-helicity momentum eigenstates have canonically defined distributional representatives on twistor space (a story that we extend to arbitrary dimension). These yield an elementary proof of the surjectivity of the Penrose transform. We give a direct construction of the twistor transform between the two different representations of massless fields on twistor space (H²$H^2$ and H³$H^3$) in which the H³$H^3$s arise as obstructions to extending the H²$H^2$s off Q$Q$ into CP⁷${\mathbb{C}\mathbb{P}}^7$.     

Conformal field theories via Hamiltonian reduction

Constraining theSL(3) WZW-model we construct a reduced theory which is invariant with respect to the new chiral algebraW ₃ ² . This symmetry is generated by the stress-energy tensor, two bosonic currents with spins 3/2 and theU(1) current. We conjecture a Kac formula that describes the highly reducible representation for this algebra. We also discuss the quantum Hamiltonian reduction for the general type of constraints that leads to the new extended conformal algebras.Address after September 1990: Lyman Laboratory, Harvard University, Cambridge, MA 02138, USA     

Conformal field theories and critical phenomena

In this article we present a brief review of the conformal symmetry and the two-dimensional conformal quantum field theories. As concrete applications of the conformal theories to the critical phenomena in statistical systems, we calculate the value of central charge and the anomalous scale dimensions of the Z ₂ symmetric quantum chain with boundary condition. The results are compatible with the prediction of the conformal field theories.     

Quantum field theories in all dimensions

In this paper we exhibit a large class of hermitian scalar field theories satisfying the Wightman axioms. For eachd>0, and each polynomialP, we exhibit a collection of theories which are loosely but legitimately based on aP() interaction ind space dimensions. One of the features of the construction is that the Wightmann-point function of each theory is a sum of finitely many integrals associated with Feynman-like graphs. Thus, it is in closed form.     

Conformal field theories and modular invariant partition functions for parafermion field theories

Parafermion conformal field theories with D_2N discrete symmetry are examined in detail. The structure of field space of parafermion field theories is studied with the help of a projection operator G. Characters of the representations of the twist sector of parafermion algebra and projected characters are given. A new class of modular invariant partition functions, therefore conformal field theories, for parafermion theories are found. We argue that the principal theories correspond to the generic critical SOS models of Andrew, Baxter and Forrest.     

Simple superconformal field theories in two dimensions

Superconformal field theories with first-order lagrangians, the super BC-systems, are considered on an arbitrary Riemann surface with an arbitrary gravitino field. The corresponding functional integrals are carefully defined, and the Weyl, supersymmetry, and holomorphic anomalies are computed. All the anomalies have a common coefficient. The holomorphic anomaly involves terms quadratic in the gravitino field.     

Conformal field theories,representations and lattice constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted andZ ₂-twisted theories, () and respectively, which may be constructed from a suitable even Euclidean lattice . Similarly, one may construct lattices and by analogous constructions from a doubly-even binary code . In the case when is self-dual, the corresponding lattices are also. Similarly, () and are self-dual if and only if is. We show that has a natural triality structure, which induces an isomorphism and also a triality structure on . For the Golay code, is the Leech lattice, and the triality on is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories () and with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.     

Internal symmetries from field theories in higher dimensions

It is suggested that a dynamical space-time symmetry group of a given non-linear relativistic theory is able to generate an internal symmetry group. It is shown that onlyO(2N-1, 1) andO(2N, 1) groups are admitted as simple dynamical symmetry groups, and they implyU(2 ^N –2) as the largest internal symmetry groups. The boson and fermion content of the considered models is determined and a new dynamical symmetry breaking mechanism, different from the spontaneous one, is introduced.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.The author would like to thank Professor J. Niederle for the kind hospitality extended to him during his stay at Bechyn.     

Gauged Lifshitz scalar field theories in two dimensions

We present two-dimensional gauged Lifshitz scalar field theories by considering the duality relation between the source current and the Noether current. Requiring the duality partially, we obtain a gauged model which recovers the bosonized Schwinger model for the IR limit. For the exact duality, however, the source current is not conserved, which means that the resulting theory is anomalous, so that the number of degrees of freedom is increased. The second model is consistently formulated by adding the Wess–Zumino type action to maintain the gauge invariance.     

Topological quantum field theories on manifolds with a boundary

We consider a class of exactly soluble topological quantum field theories on manifolds with a boundary that are invariant on-shell under diffeomorphisms which preserve the boundary. After showing that the functional integral of the two-point function with boundary conditions yields precisely the linking number, we use it to derive topological properties of the linking number. Considering gauge fixing, we obtain exact results of the partition function (Ray-Singer torsion of manifolds with a boundary) and theN-point functions in closed expressions.     

Acoustic streaming in a sound field near a free boundary

Stationary acoustic streaming that occurs near the free boundary of a compressible viscous liquid in the field of a standing sound wave excited along this boundary is theoretically investigated.     

Conformal boundary conditions and three-dimensional topological field theory

We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of Wilson graphs in a certain three-manifold, the connecting manifold. The amplitudes constructed this way can be shown to be modular invariant and to obey the correct factorization rules.     

One-point functions in perturbed boundary conformal field theories

We consider the one-point functions of bulk and boundary fields in the scaling Lee–Yang model for various combinations of bulk and boundary perturbations. The one-point functions of the bulk fields are analysed using the truncated conformal space approach and the form-factor expansion. Good agreement is found between the results of the two methods, though we find that the expression for the general boundary state given by Ghoshal and Zamolodchikov has to be corrected slightly. For the boundary fields we use thermodynamic Bethe ansatz equations to find exact expressions for the strip and semi-infinite cylinder geometries. We also find a novel off-critical identity between the cylinder partition functions of models with differing boundary conditions, and use this to investigate the regions of boundary-induced instability exhibited by the model on a finite strip.     

Finite field theories in three dimensions with and without supersymmetry

Necessary and sufficient conditions are derived for the finiteness of theS-matrix and vacuum stress of theories with Yukawa,? ³, and? ⁴ couplings in three spacetime dimensions, and general supersymmetric solutions to these conditions are given. The requirement of a finiteS-matrix allows many non-supersymmetric solutions, but with two bosons and two fermions the additional constraint of a finite vacuum stress allows only one simple alternative to supersymmetry.