An Sl(2,Z) Multiplet of Nine-Dimensional Type II Supergravity Theories

TL;DR

This paper explores the complete set of nine-dimensional type II supergravity theories obtained through generalized dimensional reductions, incorporating all S-dual branes and establishing T duality in an SL(2,Z) covariant framework.

Contribution

It introduces a comprehensive SL(2,Z) multiplet of nine-dimensional supergravity theories via generalized reductions, including all S-dual branes and their associated mass parameters.

Findings

Unified SL(2,Z) triplet of nine-dimensional theories.

Derived T duality rules for type II superstring effective actions.

Identified new KK-8A-brane and massive 11D supergravity structures.

Abstract

We show that only by performing generalized dimensional reductions all possible brane configurations are taken into account and one gets the complete lower-dimensional theory. We apply this idea to the reduction of type IIB supergravity in an SL(2,R)-covariant way and establish T duality for the type II superstring effective action in the context of generalized dimensional reduction giving the corresponding generalized Buscher's T duality rules. The full (generalized) dimensional reduction involves all the S duals of D-7-branes: Q-7-branes and a sort of composite 7-branes. The three species constitute an SL(2,Z) triplet. Their presence induces the appearance of the triplet of masses of the 9-dimensional theory. The T duals, including a ``KK-8A-brane'', which must have a compact transverse dimension have to be considered in the type IIA side. Compactification of 11-dimensional KK-9M-branes (a.k.a. M-9-branes) on the compact transverse dimension give D-8-branes while compactification on a worldvolume dimension gives KK-8A-branes. The presence of these KK-monopole-type objects breaks translation invariance and two of them given rise to an SL(2,R)-covariant ``massive 11-dimensional supergravity'' whose reduction gives the massive 9-dimensional type II theories.