Orientador: Nathan Jacob Berkovits / Coorientador: Abraham Hirsz Zimerman / Banca: Andrei Mikhailov / Banca: Nelson Braga / Banca: Victor Rivelles / Banca: Vladimir Pershin / Resumo: Primeiro vamos dar uma breve revisão sobre o artigo de Nekrasov " Lectures on curved beta-gamma systems, pure spinors, and anomalies", a fim de mostrar que o formalismo de espinor puro é livre de anomalia quando a origem é removido do espaço espinor puro. Desta forma, damos uma nova proposta para os operadores de imagem no formalismo de espinor puro mínimo. Nós calculamos amplitudes de espalhamento a nível de árvore, realizando a integração no espaço espinor puro como uma integral de Cauchy tipo multidimensional. A amplitude é escrita em termos de variáveis do espaço de espinor puro projetivo, o que é muito útil na hora de relacionar rigorosamente as versões mínima e não mínima do formalismo de espinor puro. A linguagem natural para relacionar esses formalismos é o isomorfismo de Cech-Dolbeault. Além disso, o cociclo de Dolbeault correspondente à amplitude de espalhamento a nível de árvore deve ser avaliada no espaço compacto SO(10)/SU(5) em vez de tudo o espaço de espinor puro, o que significa que a origem é removido neste espaço. Nós também obtimos uma relação entre a função de Green para um campo escalar sem massa em dez dimensões e as amplitude de espalhamento a nível de árvore. Os fatores globais constantes nas amplitudes de espalhamento são muito importante, porque eles precisam satisfazer as condições de unitariedade e S-dualidade [66]. Estes coeficientes não tinham sido computados no formalismo espinor puro, devido à dificuldade para resolver as integrais no espaço de espinores puro. Nós calculamos estas integrais usando o formalismo de espinor puro não mínimo. Assim, encontramos os coeficientes das amplitudes de um e dois-"loop" para quatro pontos sem massa. Contrastando com as dificuldades matemáticas no formalismo RNS, em que o desconhecimento das normalizações... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: First, we give a brief review about the Nekrasov's paper "Lectures on curved betagamma systems, pure spinors, and anomalies" in order to show the pure spinor formalism is anomaly free when the origin is removed from the pure spinor space. In this way we give a new proposal for the "picture lowering" operators in the minimal pure spinor formalism. We compute the tree level scattering amplitude by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude is written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the three-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. We also relate the Green's function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. The overall constan factors in the scattering amplitudes are very important because they need to satisfy the unitarity and S-duality conditions [66]. These coefficients have not been computed in the pure spinor formalism due to the difficulty to solve the integrals on the pure spinors space. We compute these integrals by using the non-minimal pure spinor formalism. So, we find the coefficients of the massless one and two-loop four-point amplitude from first principles. Contrasting with the mathematical difficulties in the RNS formalism where unknown normalizations of chiral determinant formulæ force the two-loop coefficient to be... (Complete abstract click electronic access below) / Doutor

The discovery of integrability in planar N=4 super Yang-Mills and ABJM has enabled a precise study of AdS/CFT. In the past decade integrability has been successfully applied to the spectrum of anomalous dimensions, which can now be obtained at any value of the coupling. However, in order to solve conformal field theories one also needs to understand their structure constants. Recently, there has been great progress in this direction with the all-loop proposal of Basso, Komatsu and Vieira. But there is still much to understand, as it is not yet possible to use that formalism to find structure constants of short operators at strong coupling. It is important to study wrapping corrections and resum them as the TBA did for the spectrum. It is also crucial to obtain perturbative data that can be used to check if the all-loop proposal is correct or if there are new structures that need to be unveiled. In this thesis we compute several structure constants of short operators at strong coupling, including the structure constant of Konishi with half-BPS operators. Still at strong coupling, we find a relation between the building blocks of superstring amplitudes and the tensor structures allowed by conformal symmetry. We also consider the case of extremal correlation functions and the relation of their poles to mixing with double-trace operators. We also study three-point functions at weak coupling. We take the OPE limit in a four-point function of half-BPS operators in order to shed some light on the structure of five-loop wrapping corrections of the Hexagon form factors. Finally, we take the first steps in the generalization of the Hexagon programme to other theories. We find the non-extremal setup in ABJM and the residual symmetry that it preserves, which we use to fix the two-particle form factor and constrain the four-particle hexagon. Finally, we find that the Watson equations hint at a dressing phase that needs to be further investigated.

Scherk-Schwarz reductions are a generalization of Kaluza-Klein reductions in which the higher dimensional fields are allowed to have a dependence on the compactiifed coordinates. This is possible only if the higher dimensional theory has a global symmetry and the dependence is dictated by this symmetry. In this thesis we consider generalised Scherk Schwarz reductions of supergravity and superstring theories with twists by electromagnetic dualities that are symmetries of the equations of motion but not of the action, such as the S-duality of $D=4, N=4$ super-Yang-Mills coupled to supergravity. The reduction cannot be done on the action itself, but must be done either on the field equations or on a duality invariant form of the action, such as one in the doubled formalism in which potentials are introduced for both electric and magnetic fields. The resulting theory in odd dimensions has massive form fields satisfying a self-duality condition $dA sim m*A$. We apply these methods to theories in $D=4,6,8$, and obtain new gauged supergravity theories with massive form fields, with Chern-Simons like couplings and with a scalar potential in $D=3,5,7$.

The AdS/CFT correspondence and its extensions to more general gauge/gravity dualities have provided a powerful framework for the study of strongly coupled gauge theories. This thesis explores properties of a large class of thermal strongly coupled gauge theories using the gravity dual. In order to bring the holographic framework closer to Quantum Chromodynamics (QCD), we study theories with matter in the fundamental representation. In particular, we focus on the holographic dual of SU(Nc) supersymmetric Yang-Mills theory coupled to Nf<<Nc flavours of fundamental matter at finite temperature, which is realised as Nf Dq-brane probes in the near horizon (black hole) geometry of Nc black Dp-branes. We explore many aspects of these Dp/Dq brane systems, often focussing on the D3/D7 brane system which is dual to a four dimensional gauge theory. We study the thermodynamics of the Dq-brane probes in the black hole geometry. At low temperature, the branes sit outside the black hole and the meson spectrum is discrete and possesses a mass gap. As the temperature increases, the branes approach a critical solution. Eventually, they fall into the horizon and a phase transition occurs. At large Nc and large 't Hooft coupling, we show that this phase transition is always first order. We calculate the free energy, entropy and energy densities, as well as the speed of sound in these systems. We compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations. We study the system at non-zero baryon density nb and find that there is a line of phase transitions for small nb, terminating at a critical point with finite nb. We demonstrate that, to leading order in Nf/Nc, the viscosity to entropy density ratio in these theories saturates the conjectured universal bound. Finally, we compute spectral functions and diffusion constants for fundamental matter in the high temperature phase of the D3/D7 theory.

The AdS/CFT correspondence and its extensions to more general gauge/gravity dualities have provided a powerful framework for the study of strongly coupled gauge theories. This thesis explores properties of a large class of thermal strongly coupled gauge theories using the gravity dual. In order to bring the holographic framework closer to Quantum Chromodynamics (QCD), we study theories with matter in the fundamental representation. In particular, we focus on the holographic dual of SU(Nc) supersymmetric Yang-Mills theory coupled to Nf<<Nc flavours of fundamental matter at finite temperature, which is realised as Nf Dq-brane probes in the near horizon (black hole) geometry of Nc black Dp-branes. We explore many aspects of these Dp/Dq brane systems, often focussing on the D3/D7 brane system which is dual to a four dimensional gauge theory. We study the thermodynamics of the Dq-brane probes in the black hole geometry. At low temperature, the branes sit outside the black hole and the meson spectrum is discrete and possesses a mass gap. As the temperature increases, the branes approach a critical solution. Eventually, they fall into the horizon and a phase transition occurs. At large Nc and large 't Hooft coupling, we show that this phase transition is always first order. We calculate the free energy, entropy and energy densities, as well as the speed of sound in these systems. We compute the meson spectrum for brane embeddings outside the horizon and find that tachyonic modes appear where this phase is expected to be unstable from thermodynamic considerations. We study the system at non-zero baryon density nb and find that there is a line of phase transitions for small nb, terminating at a critical point with finite nb. We demonstrate that, to leading order in Nf/Nc, the viscosity to entropy density ratio in these theories saturates the conjectured universal bound. Finally, we compute spectral functions and diffusion constants for fundamental matter in the high temperature phase of the D3/D7 theory.

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 124-130).

Made available in DSpace on 2016-05-17T16:50:53Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-03-12. Added 1 bitstream(s) on 2016-05-17T16:54:30Z : No. of bitstreams: 1 000855920.pdf: 373167 bytes, checksum: db4fc619e0ae927d8463d2bfc84a0917 (MD5) / Apresentamos o formalismo de espinores puros da supercorda. Fazemos um estudo sistemático da prescrição para o cálculo de amplitudes em nível árvore nesse formalismo. Discutimos brevemente a supercorda em Ad'S IND 5' x 'S POT. 5' / We present the pure spinor formalism of the superstring. We systematically study the prescription for tree level amplitudes in this formalism. We discuss briefly the superstring in Ad'S IND 5' x 'S POT 5'

Orientador: Nathan Jacob Berkovits / Banca: Horatiu Stefan Nastase / Banca: Vladimir Demyanovich Pershin / Resumo: A presente dissertação trata-se de uma revisão sobre amplitudes MHV na teoria de Yang-Mills e em sua extensão maximalmente supersimétrica. A demonstração da fórmula geral para tais amplitudes é dada no terceiro capítulo. Uma vez que o formalismo de twistors se apresenta como um interessante arcabouço teórico para o estudo de tais amplitudes, uma discussão sobre o mesmo e considerada, bem como sua extensão supersimétrica. Ao final, o cálculo de quatro e cinco pontos para amplitudes MHV em teoria de supercordas é apresentado. Para tal, foi utilizada a prescrição fornecida por Berkovits e Maldacena em [11] / Abstract: In the present work, we have provided a review about MHV amplitudes in Yang- Mills and maximally supersymmetric Yang-Mills theory. A proof of MHV formula was given in the third chapter. Since twistor formalism provides an interesting framework to study such amplitudes, a discussion about it is also considered as well as its supersymmetric extension. At the end, we have computed MHV four-point and ve-point gluon tree amplitudes in superstring theory, using a prescription given by Berkovits and Maldacena [11] / Mestre

Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2001-06Bitstream added on 2014-06-13T19:47:10Z : No. of bitstreams: 1 echevarria_cat_me_ift.pdf: 657711 bytes, checksum: d365934122a9e19d3c69fab3a408cda4 (MD5) / Primeiramente apresenta-se uma breve descrição das teorias de primeira quantização covariante da corda bosônica, supercorda RNS e GS. Também apresentamos a descrição topológica da supercorda. Em seguida , fazemos uma introdução à teoria clássica de campos da corda bosônica aberta formulado por Witten. Depois, consideramos a toeria clássica de campo de supercorda aberta que usa as variáveis RNS. Discutimos o problema da divergência que surge em termos de contato relacionados com picture. O formalismo topológico permite construir uma ação para teoria de campos de supercorda que é do tipo WZW. Esta ação resolve o problema da divergência. Este fato é verificado com cálculo explícito da amplitude de espalhamento para quatro estados externos na camada da massa. Seguidamente, discutimos as branas não BPS, condensação do táquion e construimos os vértices com projeção GSO negativo para o táquion e o férmion não massivo usando variáveis híbridas. Finalmente incluimos o setor GSO (-) da supercorda numa ação generalizada do tipo WZW. / Firstly we present a brief description of the covariant first quantized theories of string, RNS and GS superstring. Also we present a topological description of the superstring. Then we give an introduction to the classical open string field theory formulated by Witten. After that we cosnider the classical open superstring field theory using the RNS variables, we discuss the problem of the divergence that appears in contact terms that is related with picture. The topological formalism allow us to construct an action for the open superstring field theory which is WZW-like. This action solves the divergence problem, and we verify this fact by explicit computation of the scttering amplitude for four external on-shell states. Next, we discuss nonBPS D-branes, tachyon condensation and construct the GSO negative projected vertices for the tachyona and the massless fermion using hybrid variables. Finally we include the GSO (-) sector of the superstring in a generalized WZW-like action.

Orientador: Nathan Jacob Berkovits / Banca: Vladimir Demyanovich / Banca: Abraham Hirsz Zimerman / Resumo: Apresentamos o formalismo de espinores puros da supercorda. Fazemos um estudo sistemático da prescrição para o cálculo de amplitudes em nível árvore nesse formalismo. Discutimos brevemente a supercorda em Ad'S IND 5' x 'S POT. 5' / Abstract: We present the pure spinor formalism of the superstring. We systematically study the prescription for tree level amplitudes in this formalism. We discuss briefly the superstring in Ad'S IND 5' x 'S POT 5' / Mestre