Geometry of two-dimensional superconformal field theories

Baranov, M. A.; Frolov, I. V.; Shvarts, A. S.

doi:10.1007/bf01017011

Cited by 40 publications

(29 citation statements)

References 8 publications

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“…In analogy with the super-calculus [11], [12] the inverse operator D −1 (defined up to a constant independent of z and θ)…”

Section: Paraconformal Transformationsmentioning

confidence: 99%

“…The super-analytic maps (1.6), (1.7) are called superconformal transformations when the superderivative transforms homogeneously (see e.g. [11], [12]). This requirement, similar to (1.2), can be written in the form 9) and leads to certain restrictions on the parameter functions, namely,…”

Section: Introductionmentioning

confidence: 99%

“…This group is well-studied in connection with the theory of the superconformal manifolds and is the main tool in constructing two-dimensional superconformal field theories [11], [12]. One can solve the equations (1.10) and so find finite superconformal transformations.…”

Section: Introductionmentioning

confidence: 99%

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Para-Grassmann Extensions of the Virasoro Algebra

Филиппов

Исаев

Kurdikov

1993

Int. J. Mod. Phys. A

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The paragrassmann differential calculus is briefly reviewed. Algebras of the transformations of the para-superplane preserving the form of the parasuperderivative are constructed and their geometric meaning is discussed. A new feature of these algebras is that they contain generators of the automorphisms of the paragrassmann algebra (in addition to Ramond-Neveu-Schwarz -like conformal generators). As a first step in analyzing these algebras we introduce more tractable multilinear algebras not including the new generators. In these algebras there exists a set of multilinear identities based on the cyclic polycommutators. Different possibilities of the closure are therefore admissible. The central extensions of the algebras are given. Their number varies from 1 to [ p+1 2 ] depending on the form of the closure chosen. Finally, simple explicit examples of the paraconformal transformations are given.

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“…In analogy with the super-calculus [11], [12] the inverse operator D −1 (defined up to a constant independent of z and θ)…”

Section: Paraconformal Transformationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Para-Grassmann Extensions of the Virasoro Algebra

Филиппов

Исаев

Kurdikov

1993

Int. J. Mod. Phys. A

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“…We will call sections of A p,q " p 2 , q 2 -differentials" to distinguish them from "(p, q)-forms", the sections of Ω p,q . We can define an operator∂ from A p,0 to A p,1 using (2.2) and 6) and similarly for∂. This yields the sequences…”

Section: The∂ Operator and Its Cohomologymentioning

confidence: 99%

“…Superdifferentials were introduced in [3] and [6]. We also draw the reader's attention to the papers [7] , [8] , where bundles and jacobians are also discussed; some of the results here were independently given in [8].…”

Section: Introductionmentioning

confidence: 99%

Line bundles on super Riemann surfaces

Giddings

1988

Commun.Math. Phys.

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We give the elements of a theory of line bundles, their classification, and their connec-tions on super Riemann surfaces. There are several salient departures from the classicalcase. For example, the dimension of the Picard group is not constant, and there is nonatural hermitian form on Pic. Furthermore, the bundles with vanishing Chern numberaren't necessarily flat, nor can every such bundle be represented by an antiholomorphicconnection on the trivial bundle. Nevertheless the latter representation is still useful ininvestigating questions of holomorphic factorization. We also define a subclass of all con-nections, those which are compatible with the superconformal structure. The compatibilityconditions turn out to be constraints on the curvature 2-form. We give the elements of a theory of line bundles, their classification, and their connections on super Riemann surfaces. There are several salient departures from the classical case. For example, the dimension of the Picard group is not constant, and there is no natural hermitian form on Pic. Furthermore, the bundles with vanishing Chern number aren't necessarily flat, nor can every such bundle be represented by an antiholomorphic connection on the trivial bundle. Nevertheless the latter representation is still useful in investigating questions of holomorphic factorization. We also define a subclass of all connections, those which are compatible with the superconformal structure. The compatibility conditions turn out to be constraints on the curvature 2-form.12/87.

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Introduction

Keßler¹

2019

Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional

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Geometry of two-dimensional superconformal field theories

Cited by 40 publications

References 8 publications

Para-Grassmann Extensions of the Virasoro Algebra

Para-Grassmann Extensions of the Virasoro Algebra

Line bundles on super Riemann surfaces

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