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45
On the structure of graded symplectic supermanifolds and Courant Algebroids
, 2002
"... This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudoEuclidean vector bundles E → M0 by canonically associating to such a bundle a graded symplectic supermanifold (M, Ω), with de ..."
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Cited by 119 (3 self)
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This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudoEuclidean vector bundles E → M0 by canonically associating to such a bundle a graded symplectic supermanifold (M, Ω), with deg(Ω) = 2. Conversely, every such manifold arises in this way. We describe the algebra of functions on M in terms of E and show that “BRST charges ” on M correspond to Courant algebroid structures on E, thereby constructing the standard complex for the latter as a generalization of the classical BRST complex. As an application of these ideas, we prove the acyclicity of “higher de Rham complexes”, a generalization of a classic result of FröhlicherNijenhuis, and derive several easy but useful corollaries.
AKSZBV formalism and Courant algebroidinduced topological field theories
 Lett. Math. Phys
"... Abstract. We give a detailed exposition of the AlexandrovKontsevichSchwarzZaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a threedimensional topological sigmamodel. Using the AK ..."
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Cited by 55 (0 self)
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Abstract. We give a detailed exposition of the AlexandrovKontsevichSchwarzZaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a threedimensional topological sigmamodel. Using the AKSZ formalism, we construct the BatalinVilkovisky master action for the model. 1. Intro and Brief History. The standard procedure for quantizing classical field theories in the Lagrangian approach is by using the Feynman path integral. From the mathematical standpoint this is somewhat problematic, as it involves “integration ” over the infinitedimensional space of field configurations, on which no sensible measure has been found to exist. Nevertheless, the procedure can be made rigorous in the perturbative approach, provided the classical theory does not have too many symmetries (“too many ” means, roughly speaking, an infinitedimensional space). In the presence of these gauge symmetries, however, the procedure needs to be modified, as one has to integrate over the space of gaugeequivalence classes of field configurations.
On the AKSZ formulation of the Poisson sigma model
 56 (2001) 163, math.QA/0102108. 88 A. Connes, Noncommutative geometry
, 1994
"... Abstract. We review and extend the Alexandrov–Kontsevich– Schwarz–Zaboronsky construction of solutions of the Batalin–Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin ..."
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Cited by 36 (5 self)
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Abstract. We review and extend the Alexandrov–Kontsevich– Schwarz–Zaboronsky construction of solutions of the Batalin–Vilkovisky classical master equation. In particular, we study the case of sigma models on manifolds with boundary. We show that a special case of this construction yields the Batalin–Vilkovisky action functional of the Poisson sigma model on a disk. As we have shown in a previous paper, the perturbative quantization of this model is related to Kontsevich’s deformation quantization of Poisson manifolds and to his formality theorem. We also discuss the action of diffeomorphisms of the target manifolds. 1.
Nongeometric Backgrounds and the First Order String Sigma Model
, 906
"... We study the first order form of the NS string sigma model allowing for worldsheet couplings corresponding on the target space to a bivector, a twoform and an inverse metric. Lifting the topological sector of this action to three dimensions produces several WessZumino like terms which encode the ..."
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Cited by 28 (1 self)
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We study the first order form of the NS string sigma model allowing for worldsheet couplings corresponding on the target space to a bivector, a twoform and an inverse metric. Lifting the topological sector of this action to three dimensions produces several WessZumino like terms which encode the bivector generalization of the Courant bracket. This bracket may be familiar to physicists through the (Hijk,F k ij,Qjk i,Rijk) notation for nongeometric backgrounds introduced by SheltonTaylorWecht. The nongeometricity of the string theory in encoded in the global properties of the bivector, when the bivector is a section then the string theory is geometric. Another interesting situation emerges when one considers membrane actions which are not equivalent to string theories on the boundary of the membrane. Such a situation arises when one attempts to describe the socalled Rspace (the third Tdual of a T 3 with H3 flux). This model appears to be, at least classically, described by a membrane sigma model, not a string theory. Examples of geometric backgrounds with bivector couplings and nonvanishing Qcoefficients are provided by gauged WZW models. 1
Poisson sigma models and deformation quantization
, 2001
"... This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplec ..."
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Cited by 27 (0 self)
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This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the noncommutativity of the string endpoint coordinates. We also review the perturbative Lagrangian approach and its connection with Kontsevich’s star product. Finally we comment on the relation between the two approaches.
Dbrane dynamics and Dbrane categories
 JHEP
"... This is a short nontechnical note summarizing the motivation and results of my recent work on Dbrane categories. I also give a brief outline of how this framework can be applied to study the dynamics of topological Dbranes and why this has a bearing on the homological mirror symmetry conjecture. T ..."
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Cited by 26 (12 self)
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This is a short nontechnical note summarizing the motivation and results of my recent work on Dbrane categories. I also give a brief outline of how this framework can be applied to study the dynamics of topological Dbranes and why this has a bearing on the homological mirror symmetry conjecture. This note can be read without any
Brane/antibrane systems and U(NM) supergroup,” arXiv:hepth0101218. 45
, 2000
"... We show that in the context of topological string theories N branes and M antibranes give rise to ChernSimons gauge theory with the gauge supergroup U(NM). We also identify a deformation of the theory which corresponds to brane/antibrane annihilation. Furthermore we show that when N = M all open ..."
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Cited by 24 (2 self)
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We show that in the context of topological string theories N branes and M antibranes give rise to ChernSimons gauge theory with the gauge supergroup U(NM). We also identify a deformation of the theory which corresponds to brane/antibrane annihilation. Furthermore we show that when N = M all open string states are BRST trivial in the deformed theory. January
Offshell Gauge Fields from BRST Quantization
, 2006
"... We propose a construction for nonlinear offshell gauge field theories based on a constrained system quantized in the sense of deformation quantization. The key idea is to consider the starproduct BFV–BRST master equation as an equation of motion. The construction is formulated in terms of the BR ..."
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Cited by 20 (11 self)
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We propose a construction for nonlinear offshell gauge field theories based on a constrained system quantized in the sense of deformation quantization. The key idea is to consider the starproduct BFV–BRST master equation as an equation of motion. The construction is formulated in terms of the BRST extention of the unfolded formalism that can also be understood as an appropriate generalization of the AKSZ procedure. As an application, we consider a very simple constrained system, a quantized scalar particle, and show that it gives rise to an offshell higherspin gauge theory that automatically appears in the parent form and properly takes the familiar trace constraint into account. In particular, we derive a geometrically transparent form of the offshell higherspin theory on