Seminars (in alphabetical order):

1)Antônio Roberto da Silva (UFRJ, Brazil, with Franciscus J. Vanhecke and Cássio Sigaud)

On the Quantum Disc and the Equivalence of Morse-Smale Systems

Abstract: The purpose of this talk is to throw some new light on two fundamentals results of the early seventies, namely Peixoto's classification of Morse-Smale systems on two-dimensional manifolds, and Berezin’s concept of quantization. Though completed only in the nineties by Oshemkov and Sharko Peixoto's classification has led to many startling results. On the other hand, Berezin's quantization has recently allowed the construction of  “quantum manifolds” such as the quantum disc. We shall show that these two seemingly unrelated results in classical, respectively quantum, dynamics do have a connection.

2)Carlos Alberto Santos de Almeida (UFC, Ceará, Brazil, with Makarius Tahim)

Topological Gravity, the Hierarchy Problem and Axion Physics

Abstract: in the last years higher dimensional physics has won importance. Despite the superstrings, higher dimensional effects, in measurable scales of energy (some TeV), became only possible with Randall-Sundrum models (RS). In particular, recent studies in neutrino and axion physics have proposed new and interesting questions about neutrino mixings and new scales intermediating the Weak and Planck scales. In this work we discuss field theoretic models that in some aspects are similar to the RS models. Indeed, our models contain domain walls, solitonic-like objects that mimics the branes of the RS models. Applications are discussed ranging from topological field theories in higher dimensions until models containing $D=5$ space-time torsion in the RS scenario. In particular, we talk about subjects related to topological gravity, the hierarchy problem and axion physics. The topological terms studied are generalizations for $D>4$ of the axion-foton coupling in $D=4$. The non-abelian case is treated by means of the $\Theta$-term of QCD and generalizations for $D>4$. Such procedure involves naturally the Kalb-Ramond field. By dimensional reductions we obtain topological terms of the $B\wedge F$ type in $D=4$ Chern-Simons-like and $B\wedge\partial\varphi$ type both in $D=3$.

3)Cássius Anderson Miquele de Melo (IFT/UNESP, São Paulo, Brazil, with R. Casana and B. M. Pimentel)

Scalar and Vector Massive Fields in Lyra´s Manifold

Abstract: the problem of coupling between spin and torsion is analysed from a Lyra´s manifold background for scalar and vector massive fields using the Duffin-Kemmer-Petiau (DKP) theory. We found the propagation of the torsion is dynamical, and the minimal coupling of DKP field corresponds to a non-minimal coupling in the standard Klein-Gordon-Fock and Proca approachs. The origin of this differences in the couplings is discussed in terms of equivalence by surface terms.


4)Damiano Anselmi (Univ. di Pisa, Italy)

Irreversibility of the RG Flow in Dimensions Greater than Two

Abstract: I discuss issues concerning the generalization of Zamolodchikov's c theorem to quantum field theories in dimensions greater than two and present a framework that offers an understanding to the problem and a possible solution. I derive some predictions from this approach and check their agreement with present knowledge. I emphasize the differences between even and odd dimensions and discuss connections with certain mathematical notions such as the length of the RG flow and the distance between fixed points.

5)Fernando Haas (Unisinos, Rio Grande do Sul, Brazil, with L. G. Garcia, L. P. L. de Oliveira and J. Goedert)

Quantum Zakharov Equations

Abstract: the nonlinear interaction between Langmuir and ion-acoustic waves in quantum plasmas is shown to be described by modified Zakharov equations. In comparison with the classical Zakharov equations,the quantum Zakharov equations have additional terms depending on a quantum parameter H, which is the ratio between the ion plasmon and the electron thermal energies. The quantum Zakharov equations describe a variety of wave-wave interactions in quantum plasmas, in particular concerning modulational instabilities. Quantum diffraction tend to suppress the energy transfer from high
frequency to low frequency waves, yielding a smaller set of linearly unstable wave numbers, with a smaller growth rate. On the nonlinear realm, the adiabatic limit of the one-dimensional quantum Zakharov equations is shown to be not the nonlinear Schrödinger equation. Therefore, quantum effects seems to be an obstacle for the existence of soliton solutions in plasmas. In the same spirit, the quantum terms breaks down a conformal symmetry leading to self-similar solutions in the classical case.


6)Henrique Boschi Filho (UFRJ, Rio de Janeiro, Brazil, with Nelson Ricardo de Freitas Braga)

Scattering of Glue Balls and the AdS/CFT correspondence

Abstract: The AdS/CFT correspondence is an exact duality between string theory in anti-de Sitter space and conformal field theories on its boundary. Inspired in this correspondence some relations between strings and non conformal field theories have been found. Exact dualities in the non conformal case are intricate but approximations can reproduce important physical results. A simple approximation consists in taking just a slice of the AdS space with a size related to an energy scale. Here we will discuss how this approach can be used to reproduce the scaling of high energy Glueballs scattering amplitudes. Also we show that very simple estimates for glueball mass ratios can emerge from such an approximation.

7)José Abdalla Helayël Neto (CBPF, Rio de Janeiro, Brazil, with Andrei Bytsenko and Maria Emília Xavier Guimarães)

Hyperbolic Space Forms and Orbifold Compactification in M-Theory

Abstract: we analyze solutions of string theory and supergravity which involve real hyperbolic spaces. Examples of string compactifications are given in terms of hyperbolic coset spaces of finite volume $\Gamma\backslash {\mathbb H}^N$, where $\Gamma$ is a discrete group of isometries of ${\mathbb H}^N$. We describe finite flux, exterior forms and the tensor kernel associated with hyperbolic spaces of finite volume. The case of arithmetic geometry of $\Gamma = SL(2, {\mathbb Z}+i{\mathbb Z})$ is analyzed in details. We discuss supersymmetry surviving for supergravity solutions involving real hyperbolic space factors, string-supergravity correspondence and holography principle for a class of conformal field theories.

8)Marco Aurelio Cattacin Kneipp (UERJ, Rio de Janeiro, Brazil)

BPS Strings, String Tensions and Confinement in Super Yang-Mills 
Theories 

Abstract: we review some recent developments on BPS string solutions and monopole confinement in the Higgs phase of super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of the string flux, which allows the monopole confinement. Moreover, a bound for threshold lenght of the string breaking is obtained. When the gauge group SU(N) is broken to Z_N, the BPS string tension satisfies the Casimir scaling law. Furthermore, in the SU(3) case, the string solutions are such that they allow the formation of a confining system with three monopoles.

9)Marcus Venicius Cougo Pinto (UFRJ, Rio de Janeiro, Brazil)

How to Quantize $\kappa$-Deformed Field Theories

Abstract: we discuss some of the results and difficulties in quantizing $\kappa$-deformed field theories. Usual canonical quantization leads to the usual expression for the vaccum energy used in the literature for obtaining the Casimir effect. The same result is obtained by using the functional definition of effective action.

10)Maria Cristina Batoni Abdalla (IFT/UNESP, São Paulo, Brazil)

Perspectives of TFD on String Theory

Abstract: the Thermofield Dynamics (TFD) is developed in order to study (super)strings at thermal equilibrium. The main characteristic of TFD approach is the construction of a thermal Fock space as 
well as thermal operators. Owing to this operator characteristic, we show that the TFD may be a powerful tool to study string-gauge dualities and to identify new degrees of freedom at high temperature. To this end we extend the formalism to study (super)string in a pp-wave background. Also, we give a topological interpretation for TFD applications in the case of closed strings and show that the thermal vacuum is a kind of boundary state. Finally it is shown how the formalism could be used to investigate string interactions and string field theory at finite temperature.

11)Nami Fux Svaiter (CBPF, Rio de Janeiro, Brazil)

The Partition Function for Anharmonic Oscillator in the Strong-Coupling Regime

Abstract: we consider a single anharmonic oscillator in the strong-coupling regime.Assuming that the system is in thermal equilibrium with a reservoir, and using the strong-coupling perturbative expansion we obtain the partition function and all the thermodinamics quantities of the system. To obtain these results we follow two steps. First we must give meaning to the first term of the strong-coupling perturbative expansion, i.e., the static ultra-local generating functional.Second, we have to regularize and renormalize a kernel integrated over Euclidean time. In order to solve both problems, we make use of a combination of Klauder representation for the static ultra-local generating functional and the generalized zeta-function method.We are showing that the thermodinamics quantities are nonanalytic in the coupling constant.

12)Roldão da Rocha (UNICAMP, São Paulo, Brazil, with Jayme Vaz)

Twistors, Generalizations and Exceptional Structures

Abstract: in recent developments twistor theory has been used to describe conformal supergravity from the twistor-string formulation. It is known that twistors are closely related to spin 3/2 massless particles, which field equations are consistent if the space of conserved charges is the twistor one. We review the Penrose of twistors from the point of view of the Clifford algebras and use the paravector model of spacetime, constructing a formalism that uses the least algebraic structure that describes relativistic field theories. We use the modulo (1,1) periodicity theorem of Clifford algebras to describe the conformal transformations as linear transformations, using the method of complexification of the spacetime Clifford algebra and define twistors as a particular class of algebraic spinors. We consider some possible generalizations.

13)Salahoddin Shokranian (UnB, Distrito Federal, Brazil)

Hecke correspondences for non-connected groups: topological trace formula

Abstract: we plan to explain a trace formula for Hecke correspondences on the Weighted Cohomology for non-connected algebraic groups.

14)Sergey D. Odintsov (ICREA/IEEC, Barcelona, Spain, with S. Nojiri)

Consistent Modified Gravity and Cosmic Acceleration.

Abstract: the number of gravity theories are considered where lagrangian contains the terms growing with the decrease of the scalar curvature. Simplest example is (inconsistent) 1/R gravity and its consistent
generalization by higher derivative terms.Their cosmological properties are investigated. Such models eliminate the need in the dark energy, as correspondent gravitational terms are responsible for cosmic acceleration. The string/M-theory origin of such effective gravities is shown. The resolution of the appearing instabilities by the introduction of higher derivative terms also important for early time inflation is outlined. The appearence of minimal curvature in the universe is outlined.

15)Sebastião Alves Dias (CBPF, Rio de Janeiro, Brazil, with Marcello Barbosa da Silva Neto)

Fixing Ambiguities in QED_2 Considered in Non-Trivial Topology Sectors

Abstract: we study bosonization ambiguities in two dimensional quantum electrodynamics in the presence of topologically charged gauge fields. The computation of fermionic correlation functions suggests that ambiguities may be absent in nontrivial topologies, provided that we do not allow changes of sector as we evaluate functional integrals. This removes an infinite arbitrariness from the theory.


16)Sérgio Joffily (CBPF, Rio de Janeiro, Brazil)

Riemann Zeta Function and Vacuum Spectrum

Abstract: a variant for the Hilbert and Polya spectral interpretation of the Riemann zeta function is proposed. Instead of looking for a self-adjoint linear operator H, whose spectrum coincides with the Riemann zeta zeros, we look for complex poles of the S matrix such that by a given transformation they are all mapped into the critical line in coincidence with the nontrivial Riemann zeroes. The associated quantum system being interpreted as the quantum vacuum.


17)Valery Obukhov (Tomsk Pedagogical University, Russia) 

Variables separation in gravity

Abstract: some results on solutions of equations of gravitational theories via separation of variables are presented.

18)Vanessa Carvalho de Andrade (UnB, Distrito Federal, Brazil, with H. I. Arcos and J. G. Pereira)

Torsion and Gravitation: A New View

Abstract: according to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Though equivalent, they act differently: curvature yields a geometric description, in which the concept of gravitational force is absent whereas torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless particle equation of motion (which would represent a gravitational force) is always zero in the geometric description, but not in the teleparallel case. This means that the gravitational coupling prescription can be minimal only in the geometric case. Relying on this property, a new gravitational coupling prescription in the presence of curvature and torsion is proposed. It is constructed in such a way to preserve the equivalence between curvature and torsion, and its basic property is to be equivalent to the usual coupling prescription of general relativity. According to this view, no new physics is connected with torsion, which is just an alternative to curvature in the description of gravitation. An application of this formulation to the equations of motion of both a spinless and a spinning particle is discussed. Work supported by FINATEC.

19)Victor Rivelles (USP, São Paulo, Brazil)

Noncommutative Theories and Gravity

Abstract: There is a deep connection between noncommutative field theories and gravity. After the Seiberg-Witten map is performed the action for noncommutative field theories can be regarded as a coupling to a field dependent gravitational background.


20)Vladimir Mostepanenko (CBPF, Rio de Janeiro, Brazil, with G. L. Klimchitskaya)

Some Mathematical Aspects of the Lifshitz Formula for the Thermal Casimir Force

Abstract: we discuss recent controversies in application of the Lifshitz theory of the van der Waals and Casimir forces to real metals. The new rigorous derivation of the Lifshitz formula in terms of the reflection coefficients is proposed starting from the free energy of oscillator. It is demonstrated that if the reflection coefficients are expressed in terms of the dielectric permittivity of the Drude model, there arises a contradiction with thermodynamics. This contradiction is removed if the reflection coefficients are expressed in terms of the surface impedance. The physical reasons for this situation are explained.

21)Vladimir Pershin (UNIFEI, Minas Gerais, Brazil)

Gauge and Lorentz Anomalies in the Pure Spinor Formulation of the Heterotic Superstring

Abstract: the N=1 supergravity/super-Yang-Mills theory in D=10 has gauge and Lorentz anomalies which can be cancelled by Green-Schwarz mecanism for two specific gauge groups SO(32) e E8xE8. Unfortunately, the new terms that this mecanism introduces to the theory action break supersymmetry and until now it was not possible to find supersymmetrization of these terms. The covariant quantization of superstring in supergravity/super-Yang-Mills background could resolve this problem. We use the Berkovits formulation of the heterotic superstring in background fields to calculate the gauge and Lorentz anomalies of the theory in terms of superfields at the 1 loop level and find explicit form of the counterterms and redefinitions of the antisymmetric superfield that cancel the anomalies. These results can be used to construct a supersymmetric generalization of the Green-Schwarz mecanism.