S-duality and Compactification of type IIB Superstring Action

TL;DR

This paper explores how the SL(2,R) symmetry of type IIB superstring theory persists after compactification, enabling the generation of new solutions like black holes in lower dimensions.

Contribution

It provides a detailed analysis of the transformation properties of fields under SL(2,R) after compactification, and demonstrates how this symmetry can produce new string vacua and black hole solutions.

Findings

SL(2,R) invariance is maintained after compactification.

New black hole solutions are generated in 4D and 5D.

Transformation properties of fields are explicitly derived.

Abstract

The SL(2,R) invaraint ten dimensional type IIB superstring effective action is compactified on a torus to D spacetime dimensions. The transformation properties of scalar, vector and tensor fields, appearing after the dimensional reduction, are obtained in order to maintain the SL(2,R)} invariance of the reduced effective action. The symmetry of the action enables one to generate new string vacua from known configurations. As illustrative examples, new black hole solutions are obtained in five and four dimensions from a given set of solutions of the equations of motion.