Integrability and duality in two-dimensional QCD

We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type transformation we obtain an appropriate action for the description of the strong coupling limit, which is still integrable. We also prove that the model displays a complicated set of constraints, restricting the dynamics of part of the theory, but which are necessary to maintain the positive metric Hilbert space.Comment: 31 pages, plain tex prep. CERN-TH.7354/94, July 1994, with corrections in the text and reference

Exact S matrices and extended supersymmetry

In this revised version we correct some mistakes, realizing the supersymmetry algebra on the exact S matrix, taking into account several phase factros. We study the constraint imposed by supersymmetry on the exact $S$-matrix of $\Complex P^{n-1}$ model, and compute a non-trivial phase factor in the relation between the $S$-matrix and one of the supersymmetry generators. We discuss several features connected with the physical interpretation of the result. The supersymmetry current is studied in such context as well, and we find some operators appearing in the conservation equation of the supersymmetry current that might be connected with such phase factors. The relation with the literature on the subject is also discussed. hep-th/yymmnnnComment: 12 pages, plain tex, 1 figure in uuencoded file after the tex file, prep CERN-TH-7106/9

Operator solutions of two-dimensional chiral gauge theories

The exact operator solutions of two-dimensional anomaly-free chiral abelian gauge theories are obtained. We show that anomaly-cancellation conditions arise as consistency requirements of these solutions. For a certain class of flavour symmetries, fermion condensates are constructed. These are shown to violate the fermion-number conservation rule. The models are extended to include massive fermions. We propose a bosonised lagrangian for the massive theory and verify that it complies with the Gupta-Bleuler condition.Comment: 14 pages, latex fil

Loop scattering in two-dimensional QCD

Using the integrability conditions that we recently obtained in QCD$_2$ with massless fermions, we arrive at a sufficient number of conservation laws to be able to fix the scattering amplitudes involving a local version of the Wilson loop operator.Comment: 6 pages, plain tex

Integrable models: from dynamical solutions to string theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. Some integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the Bethe Ansatz solution of the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the seventieth anniversaries of Andr\'{e} Swieca (in memoriam) and Roland K\"{o}berle.Comment: 24 pages, to appear in Brazilian Journal of Physic

Gravitational Interactions of integrable models

We couple non-linear $\sigma$-models to Liouville gravity, showing that integrability properties of symmetric space models still hold for the matter sector. Using similar arguments for the fermionic counterpart, namely Gross--Neveu-type models, we verify that such conclusions must also hold for them, as recently suggested.Comment: 8 pages, final version to appear in Physics Letters B Revised version, with misprints corrected and some references adde

An Extensive Search for Overtones in Schwarzschild Black Holes

In this paper we show that with standard methods it is possible to obtain highly precise results for QNMs. In particular, secondary modes are obtained by numerical integration. We compare several results making a detailed analysis.Comment: 2 figures, revtex4 use