Pure spinors, twistors, and emergent supersymmetry

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Construction and decoding of BCH codes over finite commutative rings

BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings. © 1999 Elsevier B.V. All rights reserved.

Towards covariant quantization of the supermembrane

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d = 10 superparticle and superstring is extended to the d = 11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λ αdα where dα is the worldvolume variable corresponding to the d = 11 spacetime supersymmetric derivative and λα is an SO(10, 1) pure spinor variable satisfying λΓcλ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to type-IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving type-IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ 11λ = 0, replaces the bL 0 - b R 0 constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators. © SISSA/ISAS 2002.

Quantum consistency of the superstring

Using arguments based on BRST cohomology, the pure spinor formalism for the superstring in an AdS 5×S 5 background is proven to be BRST invariant and conformally invariant at the quantum level to all orders in perturbation theory. Cohomology arguments are also used to prove the existence of an infinite set of non-local BRST-invariant charges at the quantum level. © SISSA 2005.

Some remarks about Poincaré duality pairs

Bieri-Eckmann [6] introduced the concept of relative cohomology for a group pair (G, S), where G is a group and S is a family of subgroups of G and, by using that theory, they introduced the concept of Poincaré duality pairs (G, S) and provided a topological interpretation for such pairs through Eilenberg-MacLane pairs K(G, S, 1). A Poincaré duality pair is a pair (G, S) that satisfies two isomorphisms, one between absolute cohomology and relative homology and the second between relative cohomology and absolute homology. In this paper, we present a proof that those two isomorphisms are equivalent. We also present some calculations on duality pairs by using the cohomological invariant defined in [1] and studied in [2-4]. © 2012 Pushpa PublishingHouse.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

Harmonic superspace from the AdS5 × S5 pure spinor formalism

On-shell supergravity vertex operators in an AdS 5 × S 5 background are described in the pure spinor formalism by the zero mode cohomology of a BRST operator. After expanding the pure spinor BRST operator in terms of the AdS 5 radius variable, this cohomology is computed using $ \mathcal{N}=4 $ harmonic superspace variables and explicit super-field expressions are obtained for the behavior of supergravity vertex operators near the boundary of AdS 5. © 2013 SISSA, Trieste, Italy.

Resolução de equações algébricas por radicais

Pós-graduação em Educação Matemática - IGCE

Forma cohomológica do Teorema de Cauchy

Pós-graduação em Matemática Universitária - IGCE

Um estudo sobre certos invariantes homológicos relativos duais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Decomposição de grupos de dualidade de Poincaré, obstruções sing e invariantes cohomológicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cohomologia de grupos finitos e g-coincidências de aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cohomologia de grupos e algumas aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Forma traço sobre algumas extensões galoisianas de corpos p-Ádicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)