Type IIB Seven-brane Solutions from Nine-dimensional Domain Walls

TL;DR

The paper analyzes half--supersymmetric domain wall solutions in nine-dimensional maximal supergravity obtained via Scherk--Schwarz reductions of ten-dimensional IIA and IIB supergravity. It identifies three SL(2,R)–covariant 9D theories with superpotentials (one of which has zero potential yet nonzero superpotential) and one SO(1,1)–covariant theory lacking a superpotential, the latter yielding no domain walls. Upon uplifting, the walls become three classes of half--supersymmetric Type IIB 7--brane solutions, all related by SL(2,R) and capable of carrying all quantized 7--brane charges; D7 is among them, while R7, T7, and G7 provide new, explicit cases. The solutions are constrained by monodromy matching between scalars and Killing spinors, leading to SL(2,Z) quantization conditions that relate to the mass parameters and yield a rich set of conical space-time uplifts in special cases.

Abstract

We investigate half-supersymmetric domain wall solutions of four maximally supersymmetric D=9 massive supergravity theories obtained by Scherk-Schwarz reduction of D=10 IIA and IIB supergravity. One of the theories does not have a superpotential and does not allow domain wall solutions preserving any supersymmetry. The other three theories have superpotentials leading to half-supersymmetric domain wall solutions, one of which has zero potential but non-zero superpotential. The uplifting of these domain wall solutions to ten dimensions leads to three classes of half-supersymmetric Type IIB 7-brane solutions. All solutions within each class are related by SL(2,R) transformations. The three classes together contain solutions carrying all possible (quantised) 7-brane charges. One class contains the well-known D7-brane solution and its dual partners and we provide the explicit solutions for the other two classes. The domain wall solution with zero potential lifts up to a half-supersymmetric conical space-time.