International Journal of Modern Physics A

We review the physical properties of random surfaces from the view point of the continuum Liouville theory. We shall summarize physical motivations of this subject and the field-theoretic treatment of the random surfaces. In the case of subcritical strings propagating in less than two dimensions, a complete understanding has been obtained recently through matrix models. We discuss the Liouville theory understanding of these results by studying the correlation functions. We also discuss promising avenues of further investigations such as black holes in 2-dimensional gravity and 3- and 4-dimensional string theory which may be relevant to Ising₃ and QCD₄.

We analyze the tree structure arising from the recursive bootstrap equations, given the S matrix of the lightest particle. When S₁₁ contains only one singularity, among all possible bootstrap systems, the only ones which give rise to a consistent set of S matrices coincide with those of sine–Gordon breathers at the reduction point ξ = 2π/(2n + 1). We also present our investigation of bootstrap systems defined by an S₁₁ with a higher number of singularities. The only consistent examples we found belong to the set of minimal S matrices corresponding to Dynkin diagrams.

We propose interpreting the zero curvature condition associated with an integrable model as an anomaly equation. This can lead to the WZWN action and the associated current algebra quite readily and clarifies further the connections found between the integrable models and 2D gravity theories. We analyze, in detail, the cases SL(2, R) (KdV hierarchy), OSp(2/1) (sKdV hierarchy) and SL(3, R) (Boussinesq hierarchy) and obtain the operator product expansions of the appropriate fields. We also make some observations on the generalization of our method to SL(n, R).

A symmetrized bosonization for the SU(3) parafermion is given and extended to the case where parafermionic currents are defined on the root lattice. A vertex operator for the irreducible representation of parafermions and all of the screening operators are also found. In addition, the BRST cohomology and the character for SU(3) parafermions are discussed.

The first quantization of the D-dimensional relativistic spinning particle with the action invariant under reparametrizations and local worldline parasupersymmetric transformations is performed. The corresponding symmetry algebra is not of the Lie kind and is known as a polynomial algebra. It is found that the physical space of the massless particle is described by the strength tensors of Abelian antisymmetric gauge fields and topological gauge fields. In the special case D = 3 the Abelian Chern–Simons gauge field appears as a wave function of the particle. The generalizations to a massive parasupersymmetric spinning particle are presented.

Two-body multichannel scattering is discussed using, for pedagogical reasons, a field-theoretical model. Methods for unitarizing two-body hadronic weak decay amplitudes are considered. For illustrative purposes detailed studies are carried out for the following three cases: (i) , ωρ⁺, ϕρ⁺, (ii) D⁰ → ππ, , and (iii) , .

The two-point approximation to the effective chiral action with finite cut-off — as used to provide a low-energy soliton description of the nucleon — is studied in the limit of large soliton sizes, R. For some soliton profiles, the expectation that, in the large-R limit, the Casimir energy approaches a term linear in R with leading correction of order R⁻¹ is not fulfilled. We classify these profiles and show that the two-point approximation can be used to elucidate the true behaviour in such cases. For the linear profile, the asymptotic curve is found to run parallel to the linear kinetic energy, but displaced by an analytically computable negative constant.

We show that the vacuum theory has no nontrivial solution admitting the same symmetry as the massless pointlike particle in flat space–time. This is interpreted as a special kind of "gravitational anomaly." The "conformal" part of the theory, however, is anomaly-free and admits an entire class of these vacuum solutions.

If we use an electromagnetic field as the source of these solutions it has to be unpolarized.

I find increases in both masses of between 5 and 20 GeV, depending on the scale Λ at which the top-quark Yukawa coupling is assumed to diverge. These results are relevant to the predictions of the top-mode standard model.

We present the differential geometry formalism of the N = 2 conformal supergravity in harmonic superspace, which allows one to derive the BRST symmetry corresponding to N = 2 super-diffeomorphisms, local Lorentz transformations and local super-Weyl transformations. The extended transgression formula is used and the N = 2 superconformal anomalies are shown.

It is shown that the sequence of Jordan algebras , whose elements are the 3 × 3 Hermitian matrices over the division algebras ℝ, , ℚ and , can be associated with the bosonic string as well as the superstring. The construction reveals that the space–time symmetries of the first-quantized bosonic string and superstring actions can be related. The bosonic string and the superstring are associated with the exceptional Jordan algebra while the other Jordan algebras in the sequence can be related to parastring theories. We then proceed to further investigate a connection between the symmetries of supersymmetric Lagrangians and the transformations associated with the structure group of . The N = 1 on-shell supersymmetric Lagrangians in 3, 4 and 6-dimensions with a spin 0 field and a spin 1/2 field are incorporated within the Jordan-algebraic framework. We also make some remarks concerning a possible role for the division algebras in the construction of higher-dimensional extended objects.

An approach to quantizing discrete gauge models resembling bosonic strings in the Hamiltonian formulation is described. The case of three particles endowed with chiral structure and incorporating the symmetry T¹ ⊗ Sl (2, R)_ ⊗ Sl(2, R)_ is analyzed both in the path-integral and operator formulations. The propagator, spectrum, vacuum state and Regge trajectories are determined. The Regge trajectories are linearly rising and the spectrum is similar to one for discretized bosonic strings in space–time dimensions D ≥ 4. Possible applications to both nonperturbative string theory and bound states of relativistic quarks are outlined.