On the Gauge Fixing of the k Symmetry on AdS and Flat Background: the Lightcone Action for the Type IIb String on AdS_{5} X S_{5}

We explore all the possible ways of fixing the kappa symmetry for both branes and strings by means of a constant projector. We find that they can be classified according to their behaviour under Dirac conjugation and conjugation. This latter controls the maximum power of the fermionic variables in which the (super)vielbein can be expanded while the former determines which states cannot be described in the gauge. In particular there exists an interesting class of projectors for which vielbein are at most quadratic in the fermionic variables. As an example we compute the action for the type IIb on a AdS_{5} X S_{5} background with a lightcone-like projector; this action reduces to the usual lightcone GS string action in the flat limit.Comment: 12+1 pages, latex, no figure

Coloured Polymers

We show that non-oriented coloured polymers (self--avoiding walks with different types of links) are in the same universality class of the ordinary self--avoiding walks, while the oriented coloured are not.Comment: 8 pag., Latex, NBI-HE-93-0

Polymers and Topological Field Theory: A 2 Loop Computation

Within the Quantum Action Principle framework we show the perturbative renormalizability of previously proposed topological lagrangian \`a la Witten-Fujikawa describing polymers, then we perform a 2 loop computation. The theory turns out to have the same predictive power of De Gennes theory, even though its running coupling constants exhibit a very peculiar behaviour. Moreover we argue that the theory presents two phases , a topological and a non topological one.Comment: 17 pages with 5 figures (included), DFTT 29/9

Exact Results for the Supersymmetric G2G_2 Gauge Theories

We study the $N=1$ supersymmetric $G_2$ gauge theories with $N_f$ flavors of quarks in the fundamental vector representation. We find dynamically generated superpotentials, smooth quantum moduli space, quantum moduli space with additional mesons, non trivial IR fixed points.Comment: LaTex, 15 page

The Gross-Neveu model on the light cone

We consider the (massive) Gross-Neveu model using the light cone quantization where we solve the constraints explicitly. We show that the vacuum is trivial and that the quantization fails when $m=0$. We discuss how the running coupling constant emerges as a pure normal ordering effect in this context and the bound state equation.Comment: LaTex, 13+1 pages (1 eps Z-compressed figure included

The generalized Gross-Neveu model on the light cone

We investigate the generalized Gross-Neveu model using the discretized light cone quantization and we find that the vacuum of the bare theory is {\sl non} trivial in presence of vectorial current coupling when the simplest and most natural form of quantum constraints is used. Nevertheless the vacuum of the renormalized theory is trivial. In the thermodynamic the Bethe-Salpiter equations which are obtained contain all the terms needed to make them finite.Comment: LaTex, 13 page

Green functions and twist correlators for NN branes at angles

We compute the Green functions and correlator functions for N twist fields for branes at angles on T^2 and we show that there are N-2 different configurations labeled by an integer M which is roughly associated with the number of obtuse angles of the configuration. In order to perform this computation we use a SL(2,R) invariant formulation and geometric constraints instead of Pochammer contours. In particular the M=1 or M=N-1 amplitude can be expressed without using transcendental functions. We determine the amplitudes normalization from N -> N-1 reduction without using the factorization into the untwisted sector. Both the amplitudes normalization and the OPE of two twist fields are unique (up to one constant) when the \epsilon 1-\epsilon symmetry is imposed. For consistency we find also an infinite number of relations among Lauricella hypergeometric functions.Comment: 40 pages, 13 figures; V2 published version with misprints and a minor error correcte

Vector Induced Lattice Gauge Theories

We consider vector induced lattice gauge theories, in particular we consider the QED induced and we show that at negative temperature corresponds to the dimer problem while at positive temperature it describes a gas of branched polymers with loops. We argue that these models are critical at $D_{cr}=6$ for $N\ne\infty$ and they are {\sl not} critical for $N=\infty$.Comment: 9 Pages, plain Latex, NBI-HE-93-0