Compactifications with S-Duality Twists(15)

We consider generalised Scherk Schwarz reductions of supergravity and superstring theories with twists by electromagnetic dualities that are symmetries of the equations of motion but not of the action, such as the S-duality of D=4, N=4 super-Yang-Mills cou

=QM.Thisisamassiveself-dualityconditionforthe2kpotentialsAn 1.SuchwhereM

self-dualityconditionsinodddimensionswereintroducedin[26].Theself-dualityconstraint(4.71)impliesthemassive eldequation(suppressingnon-linearterms)

2An 1+... D DAn 1=e2γM(4.72)

2.However,theconstraint(4.71)halvesthenumberofwithmassmatrixproportionaltoM

degreesoffreedomofamassiven 1form eld.

Itisinstructivetocheckthenumberofphysicaldegreesoffreedom.Inddimensionsa

2masslesspformgauge eldAphascddegreesoffreedom,wherecsppisthebinomialcoe cient

csp=(s)!