String theory and loop space index theorems

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

Research output: Contribution to journalArticle

45 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalCommunications in Mathematical Physics
Volume111
Issue number1
DOIs
StatePublished - Mar 1987
Externally publishedYes

Fingerprint

Loop Space
Index Theorem
String Theory
string theory
theorems
Michael Francis Atiyah
Sigma Models
Euler Characteristic
Dirac Operator
Group Action
Supersymmetry
Compact Manifold
Paul Adrien Maurice Dirac
Riemannian Manifold
Genus
Signature
Calculate
supersymmetry
signatures
operators

ASJC Scopus subject areas

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

Cite this

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

In: Communications in Mathematical Physics, Vol. 111, No. 1, 03.1987, p. 1-10.

Research output: Contribution to journalArticle

Alvarez, Orlando ; Killingback, T. P. ; Mangano, Michelangelo ; Windey, Paul. / String theory and loop space index theorems. In: Communications in Mathematical Physics. 1987 ; Vol. 111, No. 1. pp. 1-10.
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