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

Non-linear Brane Dynamics in 6 Dimensions

We consider a dynamical brane world in a six dimensional spacetime containing a singularity. Using the Israel conditions we study the motion of a 4-brane embedded in this setup. We analize the brane behavior when its position is perturbed about a fixed point and solve the full non-linear dynamics in the several possible scenarios. We also investigate the possible gravitational shortcuts and calculate the delay between graviton and photon signals and the ratio of the corresponding subtended horizons.Comment: 5 pages, 2 figures. Contribution to the Proceedings of "Renormalization Group and Anomalies in Gravitation and Cosmology", Ouro Preto, Brazil, March 200

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

Scale Invariance in a Perturbed Einstein-de Sitter Cosmology

This paper seeks to check the validity of the "apparent fractal conjecture" (Ribeiro 2001ab: gr-qc/9909093, astro-ph/0104181), which states that the observed power-law behaviour for the average density of large-scale distribution of galaxies arises when some observational quantities, selected by their relevance in average density profile determination, are calculated along the past light cone. Implementing these conditions in the proposed set of observational relations profoundly changes the behaviour of many observables in the standard cosmological models. In particular, the average density becomes observationally inhomogeneous, even in the spatially homogeneous spacetime of standard cosmology, change which was already analysed by Ribeiro (1992b, 1993, 1994, 1995: astro-ph/9910145) for a non-perturbed model. Here we derive observational relations in a perturbed Einstein-de Sitter cosmology by means of the perturbation scheme proposed by Abdalla and Mohayaee (1999: astro-ph/9810146), where the scale factor is expanded in power series to yield perturbative terms. The differential equations derived in this perturbative context, and other observables necessary in our analysis, are solved numerically. The results show that our perturbed Einstein-de Sitter cosmology can be approximately described by a decaying power-law like average density profile, meaning that the dust distribution of this cosmology has a scaling behaviour compatible with the power-law profile of the density-distance correlation observed in the galaxy catalogues. These results show that, in the context of this work, the apparent fractal conjecture is correct.Comment: 18 pages, 1 figure, LaTeX. Final version (small changes in the figure plus some references update). Fortran code included with the LaTeX source. To be published in "Fractals

The Algebra of Non-Local Charges in Non-Linear Sigma Models

We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group $O(N)$. As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower.Comment: 27 pages + figures available via ftp, Plain TeX, IFUSP/P-106

Parameter inference and model comparison using theoretical predictions from noisy simulations

When inferring unknown parameters or comparing different models, data must be compared to underlying theory. Even if a model has no closed-form solution to derive summary statistics, it is often still possible to simulate mock data in order to generate theoretical predictions. For realistic simulations of noisy data, this is identical to drawing realizations of the data from a likelihood distribution. Though the estimated summary statistic from simulated data vectors may be unbiased, the estimator has variance which should be accounted for. We show how to correct the likelihood in the presence of an estimated summary statistic by marginalizing over the true summary statistic in the framework of a Bayesian hierarchical model. For Gaussian likelihoods where the covariance must also be estimated from simulations, we present an alteration to the Sellentin-Heavens corrected likelihood. We show that excluding the proposed correction leads to an incorrect estimate of the Bayesian evidence with JLA data. The correction is highly relevant for cosmological inference that relies on simulated data for theory (e.g. weak lensing peak statistics and simulated power spectra) and can reduce the number of simulations required.Comment: 9 pages, 6 figures, published by MNRAS. Changes: matches published version, added Bayesian hierarchical interpretation and probabilistic graphical mode