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Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional
Af: Enno Kessler Engelsk Paperback
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Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional
Af: Enno Kessler Engelsk Paperback

This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry. The objective is to understand its symmetries as geometric properties of super Riemann surfaces, which are particular complex super manifolds of dimension 1|1.

The first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed.

The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformations of the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them.

This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.

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This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry. The objective is to understand its symmetries as geometric properties of super Riemann surfaces, which are particular complex super manifolds of dimension 1|1.

The first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed.

The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformations of the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them.

This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.

Produktdetaljer
Sprog: Engelsk
Sider: 305
ISBN-13: 9783030137571
Indbinding: Paperback
Udgave:
ISBN-10: 3030137570
Udg. Dato: 29 aug 2019
Længde: 0mm
Bredde: 235mm
Højde: 155mm
Oplagsdato: 29 aug 2019
Forfatter(e): Enno Kessler
Forfatter(e) Enno Kessler


Kategori Differential- og Riemannsk geometri


Sprog Engelsk


Indbinding Paperback


Sider 305


Udgave


Længde 0mm


Bredde 235mm


Højde 155mm

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