### 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) |
---|---|

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Communications in Mathematical Physics |

Volume | 111 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1987 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

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

**String theory and loop space index theorems.** / Alvarez, Orlando; Killingback, T. P.; Mangano, Michelangelo; Windey, Paul.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 111, no. 1, pp. 1-10. https://doi.org/10.1007/BF01239011

}

TY - JOUR

T1 - String theory and loop space index theorems

AU - Alvarez, Orlando

AU - Killingback, T. P.

AU - Mangano, Michelangelo

AU - Windey, Paul

PY - 1987/3

Y1 - 1987/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0002914157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002914157&partnerID=8YFLogxK

U2 - 10.1007/BF01239011

DO - 10.1007/BF01239011

M3 - Article

AN - SCOPUS:0002914157

VL - 111

SP - 1

EP - 10

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -