Academic literature on the topic 'Superspace formalism'

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.

In this paper, we will analyze the ABJM theory in harmonic superspace. The harmonic superspace variables will be parametrized by the coset SU(2)/U(1) and thus will have manifest [Formula: see text] supersymmetry. We will study the quantum gauge transformations and the BRST transformations of this theory in gaugeon formalism. We will use this BRST symmetry to project out the physical subspace from the total Hilbert space. We will also show that the evolution of the [Formula: see text]-matrix is unitary for this ABJM theory in harmonic superspace.

We generalize the Drinfeld–Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in superspace. We use the method of symmetric space as well as the non-Abelian gauge technique to obtain the supersymmetric integrable hierarchies of the AKNS type from the zero curvature condition in superspace with the graded algebras, sl (n+1,n), providing the Hermitian symmetric space structure.

The system Bi2(n + 2)Mo n O6(n + 1) is described within the superspace formalism. Two superspace models are proposed for the different members of this family, depending on the parity of the parameter n. The superspace model for the odd members is constructed through the embedding of the cationic distribution of the member with n = 3, and the modification of a superspace model previously proposed for the compound Bi2MoO6. However, this model cannot be applied to the even members of the family. Performing the appropriate transformations, a suitable superspace model for the even members is obtained. The atomic structure of the different compounds of the family have been refined through the Rietveld method combining synchrotron X-ray and neutron powder diffraction data.

The supersymmetry algebra in four-dimensional Euclidean space is formulated in such a way that an SU(2) invariance of the algebra is apparent. This leads to a superfield formalism for representations of the algebra that can be adapted to harmonic superspace. Models in this harmonic superspace are quite similar to N = 2 models in four-dimensional Minkowski space.PACS Nos.: 11.30Pb, 03.65Fd

In this paper, we will analyze the breaking of Lorentz symmetry using aether superspace. We will analyze the aether deformation of a Chern–Simons theory using this deformed superspace. As this theory, will have gauge symmetry, we will add gauge and ghost terms to the original action. We will analyze the nonlinear BRST symmetry for this theory. We also analyze the quantum BRST symmetry in BV formalism.

An unconstrained superconnection formalism is used to derive in a natural way the fields and their BRST transformations in topological 2-D gravity. Anti-BRST transformations of the fields are also obtained. We also show how the usual BRST exact quantum action is anti-BRST exact.

The three dimensional N = 6 Chern-Simons-Matter theory admits a superspace formulation. In particular, a similar formalism to the very well known four dimensional N = 1 superspace formalism exists. This is the three dimensional N = 2 formalism which can be thought as a complexification of the three dimensional N = 1 formalism. In this formalism, only the N = 2 supersymmetry is realized off-shell and more extended supersymmetries may be completely hidden or may be realized as flavor symmetries which do not commute with the supercharges. There are two main advantages of this formalism over the field theory approach which are immediately observed. Firstly, ultraviolet convergence of the diagrams is improved, and it is possible to derive many non-renormalization theorems for particular or general situations due to this improvement. Secondly, for any given calculation which can be compared to an equivalent field theory calculation, the amount of diagrams which are necessary to be calculated is dramatically reduced. One of the advantages of the component approach over the superspace approach is that, due to arguments alla Poggio-Quinn, since the component approach has only classically marginal couplings, it is known to be infrared safe. In the superspace approach, these arguments are no longer valid and either d = 4 super Yang-Mills theories formulated in N = 1 superspace or d = 3 Chern-Simons theories formulated in N = 2 superspace are plagued by infrared infinities. These infrared divergencies are an artifact of the formalism and are due to the gauge propagator structure. In the most studied case, which is N = 4 super Yang-Mills in N = 1 superspace, this infrared divergencies can be hidden with a safe gauge choice, but this is not the case for more general Yang-Mills theories. As we will show in this work, the Yang-Mills propagator emerges in quantum loop corrections of Chern-Simons theories and produces the same problem of infrared divergencies as in four dimensions. This whole thesis work is devoted to the application of N = 2 superspace techniques in general and in particular to the recent and highly interesting N = 6 supersymmetric Chern-Simons-matter theory. We detail the main characteristics of the formalism itself, we motivate Chern-Simons theories and we formulate its supersymmetric version. We review the application of the formalism to the calculation of super-Feynman diagrams, the general arguments of renormalization properties, and as a working example we study the two-loop renormalization of the gauge sector with and without matter. Then, we review the infrared flow of mass deformed N = 4 Yang-Mills theory to N = 3 Chern-Simons theory so as to derive the construction of ABJ(M) theory. Its full superspace and component formulations are given and compared and the relevance of this theory as a gauge dual of M-theory is discussed. After that, we study in deepness the problem of infrared divergencies of the formalism by calculating some of its Green functions. We provide a solution to this problem by proposing a non-canonical gauge fixing procedure and we show it at work. Finally we display the full power of the formalism by calculating the four-loop correction of the anomalous dimension of long operators which are relevant in the AdS/CFT context.

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Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
A conjectura de Maldacena ou (AdS/CFT) desde a sua formulação é um dos tópicos em física de altas energias mais estudados. Uma das versões da conjectura é a dualidade entre a teoria de supercordas do tipo IIB em um background Ad'S IND. 5' × 'S POT. 5' suportado por um ?uxo Ramond-Ramond e a teoria deN = 4 super-YangMills em quatro dimensões. Embora a ação para supercordas neste background seja conhecida tanto no formalismo de Green-Schwarz como no formalismo de espinores puros, a construção explícita dos operadores de vértice da teoria em termos de supercampos é um problema em aberto. Nesta tese, os operadores de vértice do formalismo de espinores puros correspondentes aos estados de supergravidade são construídos próximos a fronteira de AdS. A conjectura prevê que todo estado na camada de massa da supercorda é dual a um operador invariante de gauge de N = 4 d = 4 super-Yang-Mills, em particular, os estados de supergravidade são duais a operadores Half-BPS. Os operadores Half-BPS e seus duais podem ser descritos como supercampos em um superespaço harmônico. Os resultados obtidos para os operadores de vértice são descritos em função desses supercampos duais de acordo com o previsto pela conjectura
The Maldacena’s conjecture or (AdS/CFT) has been one of the most studied topics in high energy physics since its formulation. One of the versions of the conjecture is the duality between the theory of type IIB superstrings in the background Ad'S IND. 5' × 'S POT. 5' supported by a Ramond-Ramond ?ux and the theory of N = 4 superYang-Mills in four dimensions. Although the action for the superstrings in this background is known both in the Green-Schwarz and in the pure spinor formalisms, an explicit super?eld construction of the vertex operators of the theory is an open problem. In this thesis, using the pure spinor formalism, we explicitly construct the vertex operators corresponding to supergravity states close to the boundary ofAdS. The conjecture predicts that every on-shell superstring state is dual to a gaugeinvariant operator of N = 4d = 4 super-Yang-Mills, in particular, the supergravity states are dual to Half-BPS operators. It is possible to describe all the Half-BPS operators and their duals as super?elds in harmonic superspace. The results for the vertex operators are described in terms of these dual super?elds in agreement with the prediction of the conjecture
FAPESP: 09/50775-3

Orientador: Nathan Jacob Berkovits
Banca: Brenno Carlini Vallilo
Banca: Andrey Yuryevich Mikhaylov
Banca: Dmitry Melnikov
Banca: Ion Vasile Vancea
Resumo: A conjectura de Maldacena ou (AdS/CFT) desde a sua formulação é um dos tópicos em física de altas energias mais estudados. Uma das versões da conjectura é a dualidade entre a teoria de supercordas do tipo IIB em um background Ad'S IND. 5' × 'S POT. 5' suportado por um fluxo Ramond-Ramond e a teoria deN = 4 super-YangMills em quatro dimensões. Embora a ação para supercordas neste background seja conhecida tanto no formalismo de Green-Schwarz como no formalismo de espinores puros, a construção explícita dos operadores de vértice da teoria em termos de supercampos é um problema em aberto. Nesta tese, os operadores de vértice do formalismo de espinores puros correspondentes aos estados de supergravidade são construídos próximos a fronteira de AdS. A conjectura prevê que todo estado na camada de massa da supercorda é dual a um operador invariante de gauge de N = 4 d = 4 super-Yang-Mills, em particular, os estados de supergravidade são duais a operadores Half-BPS. Os operadores Half-BPS e seus duais podem ser descritos como supercampos em um superespaço harmônico. Os resultados obtidos para os operadores de vértice são descritos em função desses supercampos duais de acordo com o previsto pela conjectura
Abstract: The Maldacena's conjecture or (AdS/CFT) has been one of the most studied topics in high energy physics since its formulation. One of the versions of the conjecture is the duality between the theory of type IIB superstrings in the background Ad'S IND. 5' × 'S POT. 5' supported by a Ramond-Ramond flux and the theory of N = 4 superYang-Mills in four dimensions. Although the action for the superstrings in this background is known both in the Green-Schwarz and in the pure spinor formalisms, an explicit superfield construction of the vertex operators of the theory is an open problem. In this thesis, using the pure spinor formalism, we explicitly construct the vertex operators corresponding to supergravity states close to the boundary ofAdS. The conjecture predicts that every on-shell superstring state is dual to a gaugeinvariant operator of N = 4d = 4 super-Yang-Mills, in particular, the supergravity states are dual to Half-BPS operators. It is possible to describe all the Half-BPS operators and their duals as superfields in harmonic superspace. The results for the vertex operators are described in terms of these dual superfields in agreement with the prediction of the conjecture
Doutor

In this Thesis I analyze some aspects of a class of quantum field theories that can be obtained by marginally deforming N=4 SYM theory. These theories constitue a very non trivial example of N=1 superconformal actions in four dimensional space-time and play a role in the context of AdS/CFT. I begin by introducing superfield notations and constructing deformed theories following Leigh and Strassler procedure. Then an analysis of the finiteness properties of the actions is performed. Considering different specific cases, solutions of the superconformal constraint are given. The issues of conformal invariance and finiteness in the case of complex and real beta-deformed models are addressed. In the real beta case an all loop solution of the constraint is provided. In the case of complex deformation, it turns out that the condition of vanishing beta function leads to a result which is scheme dependent. In the second part of the work, anomalous dimensions of composite operators are computed. A new method for extracting protected operators in the chiral sector is introduced. Using the proposed procedure it is possible to gain a loop order in perturbative computations with respect to canonical methods. The structure of the chiral ring of the deformed theories is then classified up to three loops.