Noncompact Symmetries in String Theory

TL;DR

This paper investigates the role of noncompact symmetries in string theory, especially in moduli spaces and effective actions, revealing their interconnected nature through dimensional reduction and world sheet analysis.

Contribution

It provides a unified analysis of noncompact symmetries in string theory from both effective field theory and world sheet perspectives, emphasizing the role of Chern--Simons terms.

Findings

Moduli spaces are described by noncompact groups modded out by compact subgroups.

Noncompact symmetries appear in effective actions for string cosmology.

Chern--Simons terms are crucial in understanding these symmetries.

Abstract

Noncompact groups, similar to those that appeared in various supergravity theories in the 1970's, have been turning up in recent studies of string theory. First it was discovered that moduli spaces of toroidal compactification are given by noncompact groups modded out by their maximal compact subgroups and discrete duality groups. Then it was found that many other moduli spaces have analogous descriptions. More recently, noncompact group symmetries have turned up in effective actions used to study string cosmology and other classical configurations. This paper explores these noncompact groups in the case of toroidal compactification both from the viewpoint of low-energy effective field theory, using the method of dimensional reduction, and from the viewpoint of the string theory world sheet. The conclusion is that all these symmetries are intimately related. In particular, we find that Chern--Simons terms in the three-form field strength $H_{\mu\nu\rho}$ play a crucial role.