Plenary Sessions:

D. Adams (Lorentz Inst., Netherlands)

Connecting the Functional Integral and Hamiltonian Frameworks for Field Theories Via Dimensional Reduction of Functional Determinants


Abstract: a method for deriving "dimensionally reduced" expressions for functional determinants is described. This is done via a partial zeta-regularisation, formally applying a general formula for the zeta-determinant of a differential operator in one variable with operator-valued coefficients. Using this, a new way to connect the functional integral and Hamiltonian frameworks for fermionic or bosonic field theories is described. It is an alternative to the usual connection (which is based on transfer matrices and requires a time discretisation) and avoids certain problematic features of that approach.

N. Berkovits  (IFT/UNESP, Brazil)

Perturbative Finiteness of Superstring Theory

Abstract: after reviewing the problems with quantizing gravity in the framework of general relativity, I will give a brief introduction to gravity in the framework of bosonic string and superstring theory. Using a recently developed formulation of superstring theory which involves pure spinors, one can simplify the proof that gravitional scattering amplitudes in superstring theory are finite order-by-order in perturbation theory.

M. Cvetic (Univ. of Penn, USA)

Supersymmetric Vacua of String Theory with Branes and Fluxes

Abstract: we review developments in string theory leading to four dimensional supersymmetric solutions with intersecting D-branes and supergravity fluxes. These solutions lead to chiral non-Abelian field theories and all the stabilization of the moduli. Implications for these solutions particle physics are addressed.

L. D. Faddeev (Steklov Inst. Math., Russia)

Evolution operators for the quantum integrable models on discrete space-time

Abstract: It was shown recently. that known integrable models on two dimensional space-time can be deformed to the lattice retaining exact integrability. In my talk I shall illustrate this on simplest examples. The main object will be the evolution operator, defining shift in discrete time over one lattice site. I shall present several exact formulas and discuss their interpretation. The notion of a modular double, which appears in this construction, will be explained.

R. Kerner (Univ. Paris VI, France)

Non-Commutative Geometry and Generalized Born-Infeld Theory

Abstract: we discuss possible generalizations of the Born-Infeld theory - first in the non-abelian case, then in the context of non-commutative geometry. Several lagrangian principles are presented, leading to certain interesting physical possibilities: new static finite-energy configurations, and a generalization of Higgs fields that may be useful in cosmological models.

C. Nuñez (Univ. of Buenos Aires, Argentina)

String Theory on AdS3

Abstract: I will discuss string theory on three dimensional Anti de Sitter spacetime. This interesting model is the simplest example of string propagation on a curved spacetime. It allows to address important questions involving the notion of time in string theory, singularities and conceptual problems of black hole physics. It is also a relevant case of the AdS/CFT duality conjecture between gauge theories and gravity since several details of the correspondence can be worked out explicitly at the string theory level. Despite the progress made in recent years several questions remain open. I will review these problems and comment on possible solutions.

J. Palis (IMPA, Brazil)

A Global Scenario for Non-Conservative Dynamics Recent Results

Abstract: we shall discuss a global conjecture on the finitude of large basin attractors and their stochastic stability: partial success, strategy and some related results on homoclinic bifurcations, dynamical robustness and partially hyperbolic systems. The aim of the conjecture is a description in a rather simple conceptual way of the long range behavior of a typical (positive) trajectory of a typical dynamical systems: a trajectory has only finitely many choices where to accumulate upon in the future.

F. Toppan (CBPF, Brazil)

Hermitian Versus Holomorphic Complex and Quaternionic Generalized Supersymmetries of the M-theory: a Classification

Abstract: relying upon the division-algebra classification of Clifford algebras and spinors, a classification of generalized supersymmetries (or, with a slight abuse of language,``generalized supertranslations") is provided. In each given space-time the maximal, saturated, generalized supersymmetry, compatible with the division-algebra constraint that can be consistently imposed on spinors and on superalgebra generators, is furnished. Constraining the superalgebra generators in both the complex and the quaternionic cases gives rise to the two classes of constrained
hermitian and holomorphic generalized supersymmetries. In the complex case these two classes of generalized supersymmetries can be regarded as complementary. The quaternionic holomorphic supersymmetry only exists in certain space-time dimensions and can admit at most a single bosonic scalar central charge.\par The results here presented pave the way for a better understanding of the various $M$ algebra-type of structures which can be introduced in different space-time signatures and in association with different division algebras, as well as their mutual relations. In a previous work, e.g., the introduction of a complex holomorphic generalized supersymmetry was shown to be necessary in order to perform the analytic continuation of the standard $M$-theory to
the $11$-dimensional Euclidean space. As an application of the present results, it is shown that the above algebra also admits a $12$-dimensional, Euclidean, $F$-algebra presentation.

F. L. Williams (Univ. of Massachussetts, EUA)

Further Thoughts on First Generation Solitons and J-T Gravity 

Abstract: we construct an explicit pair of maps inverse to each other that transform a soliton metric (defined by first generation solitons) to a black hole metric in two-dimensional Jackiw-Teitelboim (J-T) gravity-and conversely transform the latter metric to the soliton metric.Thus these maps provide for a concrete realization of an interesting observation of Gegenberg and Kunstatter.Remarkably,they turn out to be transformations of the solution spaces, also, of the field equations defined by the Laplace-Beltrami operators of these metrics.In particular,using the theory of generalized hypergeometric equations (in the sense of Nikiforov and Uvarov), we can
construct explicit solutions of the soliton field equations,under nice quantization conditions.

J. Zanelli (CECS, Chile)

11D Super Chern-Simons Action and local M Theory Algebra

Abstract: Eleven-dimensional supersymmetric theories containing gravity can be obtained as deformations of a Chern-Simons action for the $osp(32|1)$ gauge algebra. The original action is invariant under local $SO(10,2)$ (AdS), while the gravitational sector of the contracted theories possess local $ISO(10,1)$ (Poincar\'{e}) symmetry. The gravitational sectors are not described by the Einstein Hilbert action but by the dimensional continuation of the ten-dimensional Euler density. The actions for the contracted algebras possess gauge invariance under different extensions of the super Poincar\'{e} algebra, containing, apart from the generators of translations ($P_a$) and Lorentz rotations ($J_{ab}$), one supersymmetry generator ($Q$) and different combinations of a rank two and a rank five abelian generator ($Z_{ab}$ and $Z_{abcde}$), also known as M-algebra. Here we discuss how these theories are constructed and related to each other. The relation to the standard supergravity of Cremmer, Julia and Scherk is also briefly discussed.

Seminars:

(click here to see the list of invited seminars)

Posters:

(click here to see the list of posters)

Discussion: Perspectives of Mathematical Physics in Brazil and in the World

A. A. Bytsenko (UEL, Brazil)

L. D. Faddeev (St. Petersburgo, Russia)

J. A. Helayël-Neto (CBPF, Brazil)

R. Kerner (Univ. Paris VI, France)

J. Palis (IMPA, Brazil) - to be confirmed