TY - JOUR

T1 - The Dirac-Ramond operator in string theory and loop space index theorems

AU - Alvarez, Orlando

AU - Killingback, T. P.

AU - Mangano, Michelangelo

AU - Windey, Paul

N1 - Funding Information:
*Invited talk presented by P.W. at the Irvine conference on non-perturbative methods in physics. tThis work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY85-15857. Fermilab is operated by the Universities Research Association, Inc., under contract with the United States Department of Energy.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1987/9

Y1 - 1987/9

N2 - 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, p1 (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.

AB - 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, p1 (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.

UR - http://www.scopus.com/inward/record.url?scp=4243925850&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243925850&partnerID=8YFLogxK

U2 - 10.1016/0920-5632(87)90110-1

DO - 10.1016/0920-5632(87)90110-1

M3 - Article

AN - SCOPUS:4243925850

VL - 1

SP - 189

EP - 215

JO - Nuclear and Particle Physics Proceedings

JF - Nuclear and Particle Physics Proceedings

SN - 2405-6014

IS - 1

ER -