Solution--Generating Transformations and the String Effective Action

TL;DR

This paper thoroughly analyzes the solution-generating duality transformations in superstring theory's low-energy effective action, exploring their structure, extensions with gauge fields, and corrections, revealing a rich symmetry landscape.

Contribution

It provides a comprehensive classification of duality groups, including non-Abelian and Abelian cases, and examines the effects of xe9 corrections and gauge embeddings on these symmetries.

Findings

Full duality group for one isometry is (SO^{b0}(1,1))^{3} x D_{4}

Duality transformations simplify with gauge group embedding in the holonomy group

Identifies duality symmetries in Type II theories with one isometry

Abstract

We study exhaustively the solution-generating transformations (dualities) that occur in the context of the low-energy effective action of superstring theory. We first consider target-space duality (``T duality'') transformations in absence of vector fields. We find that for one isometry the full duality group is (SO^{\uparrow}(1,1))^{3} x D_{4}, the discrete part (D_{4}) being non-Abelian. We, then, include non-Abelian Yang--Mills fields and find the corresponding generalization of the T duality transformations. We study the \alpha^{\prime} corrections to these transformations and show that the T duality rules considerably simplify if the gauge group is embedded in the holonomy group. Next, in the case in which there are Abelian vector fields, we consider the duality group that includes the transformation introduced by Sen that rotates among themselves components of the metric, axion and vector field. Finally we list the duality symmetries of the Type II theories with one isometry.