### Abstract

We study index theorems for the Dirac-Ramond operator on a compact Riemannian manifold. The existence of a group action on the loop space makes possible the definition of a character valued index which we calculate by using a two-dimensional sigma model with N=1/2 supersymmetry. We compute the Euler characteristic, the Hirzebruch signature and the Dirac-Ramond genus of loop space. We compare our results to the calculations made by using the Atiyah-Singer character-valued index theorem.

Original language | English (US) |
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Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Communications in Mathematical Physics |

Volume | 111 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1987 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Alvarez, O., Killingback, T. P., Mangano, M., & Windey, P. (1987). String theory and loop space index theorems.

*Communications in Mathematical Physics*,*111*(1), 1-10. https://doi.org/10.1007/BF01239011