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

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

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)189-215
Number of pages27
JournalNuclear Physics B (Proceedings Supplements)
Issue number1
StatePublished - Sep 1987
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics


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