The Dirac-Ramond operator in string theory and loop space index theorems

Orlando Alvarez; T.P Killingback; Michelangelo Mangano; Paul Windey

doi:10.1016/0920-5632(87)90110-1

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Journal article

The Dirac-Ramond operator in string theory and loop space index theorems

Orlando Alvarez, T.P Killingback, Michelangelo Mangano and Paul Windey

Nuclear physics. Section B, Proceedings supplement, Vol.1(1), pp.189-215

1987

DOI: https://doi.org/10.1016/0920-5632(87)90110-1

Abstract

The index of the Direc-Ramond operator is computed and analyzed. It is shown to be the extension of the Atiyah-Singer index theorem for loop space. It can also be seen as a generating function for the Atiyah-Singer index for the states of the string. Its existence depends on the Green-Schwarz anomaly cancellation condition, p 1 ( M) = 0, which defines an analog of a spin structure for the loop space. One also finds topological invariants for the loop space which correspond to different twistings of the Dirac-Ramond operator. All of them can be expressed in terms of Jacobi elliptic functions.

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Title: The Dirac-Ramond operator in string theory and loop space index theorems
Creators: Orlando Alvarez - Department of Physics and Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, USA
T.P Killingback - DAMTP, University of Cambridge, England CB3 9EW
Michelangelo Mangano - Fermi National Accelerator Laboratory, Batavia, IL 60510, USA
Paul Windey - Department of Physics and Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, USA
Publication Details: Nuclear physics. Section B, Proceedings supplement, Vol.1(1), pp.189-215
Publisher: Elsevier B.V
Academic Unit: College of A&S; A&S - Physics
Language: English
Resource Type: Journal article
Record Identifier: 991031614339502976