Geometry of Dual Pairs of Complex Supercurves

Rabin, Jeffrey M.

doi:10.1007/978-3-642-21744-9_11

Cited by 1 publication

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“…Remark 2.6. We refer to [6,15,19] and references therein for usage of the term "superconformal" with regards to these vector fields.…”

Section: Preliminary Theorymentioning

confidence: 99%

“…The superparticle Lagrangian is a density defined by a certain collection of vector fields, called superconformal vector fields ( [15,19]), which are themselves subject to a certain algebraic constraintthat they satisfy the relations of a supersymmetry algebra (for its relation to physics see [17]). With these vector fields we are led to a notion of maximal superconformal structure.…”

Section: Introductionmentioning

confidence: 99%

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Superconformal Structures and the Superparticle on the Complex Projective Line

Bettadapura

2015

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In this paper the notion of a superconformal structure on a supermanifold is introduced in an effort to study the superparticle sigma-model. There are, in particular, two main aspects of the sigma-model which are investigated. The first is on the relationship between the superparticle Lagrangian and the component Lagrangian; and the second is on the problem of integrating infinitesimal variations to globally-defined variations of the component Lagrangian, which leads naturally to a notion of consistency. Throughout this paper illustrations are provided on the complex projective line. Contents1. Introduction 1 Acknowledgements 2 2. Preliminary Theory 3 2.1. Supermanifolds 3 2.2. Superconformal Structures 4 2.3. Illustrations on CP 1 5 3. The Superparticle Lagrangian and Consistency 6 3.1. The Superparticle Lagrangian 6 3.2. The Component Lagrangian 8 3.3. Consistency of the Component Lagrangian 9 4. The Superparticle on CP 1 11 4.1. A Non-Existence Result 11 4.2. Consistent fields on CP 1|2 12 4.3. Consistent fields on a non-Standard CP 1|2 13 5. Concluding Remarks 15 Appendix A. Proof of Theorem 2.10 16 References 18

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“…Remark 2.6. We refer to [6,15,19] and references therein for usage of the term "superconformal" with regards to these vector fields.…”

Section: Preliminary Theorymentioning

confidence: 99%