BRST: da quebra suave à quebra espontânea da simetria

Nesta tese falamos essencialmente sobre a simetria BRST no modelo de Gribov-Zwanziger. Estudamos a quebra suave, a quebra linear e a quebra espontânea, todas da simetria BRST. Na formulação padrão do modelo, quebrada suavemente, construímos o modelo de réplica usado para estimar os valores das massas das glueballs. Utilizando campos auxiliares construímos um modelo quebrado linearmente, e utilizando basicamente o mesmo procedimento, uma formulação mais recente onde a simetria é quebrada espontâneamente.

BRST cohomology and nonlocal conserved charges

A relation is found between nonlocal conserved charges in string theory and certain ghost-number two states in the BRST cohomology. This provides a simple proof that the nonlocal conserved charges for the superstring in an AdS 5 × S5 background are BRST-invariant in the pure spinor formalism and are κ-symmetric in the Green-Schwarz formalism. © SISSA/ISAS 2005.

Um estudo sobre a teoria de campos no espaço-tempo não comutativo

Os aspectos quânticos de teorias de campo formuladas no espaço-tempo não comutativo têm sido amplamente estudados ao longo dos anos. Um dos principais aspectos é o que na literatura ficou conhecido como mixing IR/UV. Trata-se de uma mistura das divergências, que foi vista pela primeira vez no trabalho de Minwalla et al [28], onde num estudo do campo escalar não comutativo com interação quártica vemos já a 1 loop que o tadpole tem uma divergência UV associada a sua parte planar e, junto com ela, temos uma divergência IR associada com um gráfico não planar. Essa mistura torna a teoria não renormalizável. Dado tal problema, houve então uma busca por mecanismos que separassem essas divergências a fim de termos teorias renormalizáveis. Um mecanismo proposto foi a adição de um termo não local na ação U*(1) para que esta seja estável.Neste trabalho, estudamos através da renormalização algébrica a estabilidade deste modelo. Para tal, precisamos localizar o operador não local através de campos auxiliares e seus respectivos ghosts (metodo de Zwanziger) na intenção de retirar os graus de liberdade indesejados que surgem. Usamos o approachda quebra soft de BRST para analisar o termo que quebra BRST, que consiste em reescrevermos tal termo com o auxílio de fontes externas que num determinado limite físico voltam ao termo original.Como resultado, vimos que a teoria com a adição deste termo na ação só é renormalizável se tivermos que introduzir novos termos, sendo alguns deles quárticos. Porém, estes termos mudam a forma do propagador, que não desacopla as divergências. Um outro aspecto que podemos salientar é que, dependendo da escolha de alguns parâmetros, o propagador dá indícios de termos um fótonconfinante, seguindo o critério de Wilson e o critério da perda da positividade do propagador.

Consistent deformations of [p,p]-type gauge field theories

Using BRST-cohomological techniques, we analyze the consistent deformations of theories describing free tensor gauge fields whose symmetries are represented by Young tableaux made of two columns of equal length p, p > 1. Under the assumptions of locality and Poincaré invariance, we find that there is no consistent deformation of these theories that non-trivially modifies the gauge algebra and/or the gauge transformations. Adding the requirement that the deformation contains no more than two derivatives, the only possible deformation is a cosmological-constant-like term. © SISSA/ISAS 2004.

Spin three gauge theory revisited

We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension 3$">n>3. Under the sole assumptions of Poincaré and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of either three or five derivatives and are uniquely characterized by a rank-three constant tensor (an internal algebra structure constant). The covariant cubic vertex containing three derivatives is the vertex discovered by Berends, Burgers and van Dam, which however leads to inconsistencies at second order in the deformation parameter. In dimensions 4$">n>4 and for a completely antisymmetric structure constant tensor, another covariant cubic vertex exists, which contains five derivatives and passes the consistency test where the previous vertex failed. © SISSA 2006.

Pure spinors, twistors, and emergent supersymmetry

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Taming the b antighost with Ramond-Ramond flux

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cornering the unphysical vertex

In the classical pure spinor worldsheet theory of AdS(5) x S-5 there are some vertex operators which do not correspond to any physical excitations. We study their flat space limit. We find that the BRST operator of the worldsheet theory in flat space-time can be nontrivially deformed without deforming the worldsheet action. Some of these deformations describe the linear dilaton background. But the deformation corresponding to the nonphysical vertex differs from the linear dilaton in not being worldsheet parity even. The nonphysically deformed worldsheet theory has nonzero beta-function at one loop. This means that the classical Type IIB SUGRA backgrounds are not completely characterized by requiring the BRST symmetry of the classical worldsheet theory; it is also necessary to require the vanishing of the one-loop beta-function.

Decoupling of unphysical states in the minimal pure spinor formalism II

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Pure spinor partition function and the massive superstring spectrum

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On semiclassical analysis of pure spinor superstring in an AdS(5) x S-5 background

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Multiloop superstring amplitudes from non-minimal pure spinor formalism

Using the non-minimal version of the pure spinor formalism, manifestly super-Poincare covariant superstring scattering amplitudes can be computed as in topological string theory without the need of picture-changing operators. The only subtlety comes from regularizing the functional integral over the pure spinor ghosts. In this paper, it is shown how to regularize this functional integral in a BRST-invariant manner, allowing the computation of arbitrary multiloop amplitudes. The regularization method simplifies for scattering amplitudes which contribute to ten-dimensional F-terms, i.e. terms in the ten-dimensional superspace action which do not involve integration over the maximum number of theta's.

Relating the RNS and pure spinor formalisms for the superstring

Recently, the superstring was covariantly quantized using the BRST-like operator Q = ∮ λαdα where λα is a pure spinor and dα are the fermionic Green-Schwarz constraints. By performing a field redefinition and a similarity transformation, this BRST-like operator is mapped to the sum of the Ramond-Neveu-Schwarz BRST operator and η0 ghost. This map is then used to relate physical vertex operators and tree amplitudes in the two formalisms. Furthermore, the map implies the existence of a b ghost in the pure spinor formalism which might be useful for loop amplitude computations.

Covariant quantization of the superparticle using pure spinors

The ten-dimensional superparticle is covariantly quantized by constructing a BRST operator from the fermionic Green-Schwarz constraints and a bosonic pure spinor variable. This same method was recently used for covariantly quantizing the superstring, and it is hoped that the simpler case of the superparticle will be useful for those who want to study this quantization method. It is interesting that quantization of the superparticle action closely resembles quantization of the worldline action for Chern-Simons theory.

The Ramond sector of open superstring field theory

Although the equations of motion for the Neveu-Schwarz (NS) and Ramond (R) sectors of open superstring field theory can be covariantly expressed in terms of one NS and one R string field, picture-changing problems prevent the construction of an action involving these two string fields. However, a consistent action can be constructed by dividing the NS and R states into three string fields which are real, chiral and antichiral. The open superstring field theory action includes a WZW-like term for the real field and holomorphic Chern-Simons-like terms for the chiral and antichiral fields. Different versions of the action can be constructed with either manifest d = 8 Lorentz covariance or manifest TV = 1 d = 4 super-Poincaré covariance. The lack of a manifestly d = 10 Lorentz covariant action is related to the self-dual five-form in the type-IIB R-R sector.