On the structure of unitary conformal field theory. I. Existence of conformal blocks

We study the general mathematical structure of unitary rational conformal field theories in two dimensions, starting from the Euclidean Green functions of the scaling fields. We show that, under certain assumptions, the scaling fields of such theories can be written as sums of products of chiral fields. The chiral fields satisfy an algebra whose structure constants are the matrix elements of Yang-Baxter- or braid-matrices whose properties we analyze. The upshot of our analysis is that two-dimensional conformal field theories of the type considered in this paper appear to be constructible from the representation theory of a pair of chiral algebras.     

On conformal invariance in quantum field theory

We study the transformation law of interacting fields under the universal convering group of the conformal group. It is defined with respect to the representations of the discrete series. These representations are field representations in the sense that they act on finite component fields defined over Minkowski space. The conflict with Einstein causality is avoided as in the case of free fields with canonical dimension. Furthermore, we determine the conformal invariant two-point function of arbitrary spin. Our result coincides with that obtained by Rühl. In particular, we investigate the two-point function of symmetric and traceless tensor fields and give the explicit form of the trace terms.     

On thermodynamic approaches to conformal field theory

We present the thermodynamic Bethe ansatz as a way to factorize the partition function of a 2d field theory, in particular, a conformal field theory and we compare it with another approach to factorization due to Schoutens which consists of diagonalizing matrix recursion relations between the partition functions at consecutive levels. We prove that both are equivalent, taking as examples the SU(2) spinons and the 3-state Potts model. In the latter case we see that there are two different thermodynamic Bethe ansatz equation systems with the same physical content, of which the second is new and corresponds to a one-quasiparticle representation, as opposed to the usual two-quasiparticle representation. This new thermodynamic Bethe ansatz system leads to a new dilogarithmic formula for the central charge of that model.     

On unitary implementability of conformal transformations

We show that the only projective representations of the conformal group in a Hilbert space which, when restricted to the Poincaré subgroup, are unitary irreducible of mass zero and discrete helicity, are the usual unitary representations of SU(2, 2) often called ladder representations. Some physical consequences are also discussed.     

Logarithmic conformal field theory approach to topologically massive gravity

We study the topologically massive gravity at the chiral point (chiral gravity) by using the logarithmic conformal field theory. Two new tensor fields of ψnew${\psi }^{\mathrm{new}}$ and X   are introduced for a candidate of propagating physical field at the chiral point. However, we show that (ψnew,ψL${\psi }^{\mathrm{new}},{\psi }^L$) form a dipole ghost pair of unphysical fields and X is not a primary. This implies that there is no physically propagating degrees of freedom at the chiral point.     

On the application of conformal symmetry to quantum field theory

To leading order in α_s(Q²) conformal symmetry specifies the eigensolutions of the evolution equation for meson distribution amplitudes, the wavefunctions which control large-momentum-transfer exclusive mesonic processes in QCD. We find that at next to leading order, the eigensolutions in various field theories depend on the regularization scheme, even for zero β-function. This is contrary to the expectations of conformal symmetry.     

Adelic conformal field theory

We stress the use of modular forms in obtaining adelic formulations of field theoretical problems. Supersymmetry then appears in the real section with thep-adic parts as arithmetic completions. We first show how the Casimir effect is naturally interpreted adelically and the coefficient arises from dimensional analysis. We then suggest looking at the zero slope limit of adelic string amplitudes. Finally, we interpret the rationality of the critical exponents for conformal field theories in terms of p-adic analyticity of correlation functions.     

Markov traces and II1 factors in conformal field theory

Using the duality equations of Moore and Seiberg we define for every primary field in a Rational Conformal Field Theory a proper Markov trace and hence a knot invariant. Next we define two nested algebras and show, using results of Ocneanu, how the position of the smaller algebra in the larger one reproduces part of the duality data. A new method for constructing Rational Conformal Field Theories is proposed.     

On the large N limit of conformal field theory

Following recent advances in large N matrix mechanics, I discuss here the free (Cuntz) algebraic formulation of the large N limit of two-dimensional conformal field theories of chiral adjoint fermions and bosons. One of the central results is a new affine free algebra which describes a large N limit of affine Lie algebra. Other results include the associated free-algebraic partition functions and characters, a free-algebraic coset construction, free-algebraic construction of , free-algebraic vertex operator constructions in the large N Bose systems, and a provocative new free-algebraic factorization of the ordinary Koba-Nielsen factor.     

Rationality in conformal field theory

We show that if the one-loop partition function of a modular invariant conformal field theory can be expressed as a finite sum of holomorphically factorized terms thenc and all values ofh are rational.     

Logarithmic conformal field theory through nilpotent conformal dimensions

We study logarithmic conformal field theories (LCFTs) through the introduction of nilpotent conformal weights. Using this device, we derive the properties of LCFTs such as the transformation laws, singular vectors and the structure of correlation functions. We discuss the emergence of an extra energy momentum tensor, which is the logarithmic partner of the energy momentum tensor.     

A conformal holomorphic field theory

A formulation of a field theory on the complex Minkowski space in terms of complex differential geometry is proposed. It is also shown that our model of field theory differs from the standard model on the real Minkowski space only in the limit of high energy.     

Two-dimensional conformal quantum field theory

On leave of absence from the Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria.     

On the structure of planar field theory

Universality of the ω intercept has been recently questioned, on the basis of new and precise high-energy data for theK _L ⁰ total cross-sections and regeneration amplitudes on various nuclei. These data are re-analysed within the framework of Glauber's theory, with special attention to the contribution of inelastic intermediate states. They are shown to be completely understandable using standard values for all parameters, including the ω intercept. The analysis determines the characteristics of inelastic collisions of Kaons in nuclei: the diffractive terms could have been deduced from other sources, but this is the first evaluation of ω-exchange terms in nuclei.