## Abstract

A number of issues concerning affine Lie algebras and string propagation on group manifolds are addressed. We show that a 1 + 1 dimensional quantum field theory which gives a realization of current algebra (for any non-abelian Lie group G) will always give rise to an "integrable" representation. It is known that string propagation on the group manifold can give rise to a realization of current algebra for any G and any k, but precisely which representations occur for given k has not been determined previously. We do this here by studying modular invariance and by making a semiclassical study for large k. These results permit a complete description of the operator product algebra. Some examples based on SO(3) and SU(3)/Z_{3} are worked out in detail.

Original language | English (US) |
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Pages (from-to) | 493-549 |

Number of pages | 57 |

Journal | Nuclear Physics, Section B |

Volume | 278 |

Issue number | 3 |

DOIs | |

State | Published - Dec 15 1986 |

## All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics