Compactifications with S-Duality Twists

TL;DR

The paper addresses compactifications twisted by dualities that act on field equations but not on the action, and introduces a doubled formalism to render dualities as action symmetries. By performing Scherk-Schwarz type reductions with duality twists, it shows that the resulting theories in odd dimensions contain massive self-dual form fields and are classified by conjugacy classes of the duality group. The approach is applied to reductions from $d=8,6,4$ supergravity, yielding $D=3,5,7$ gauged supergravities with Chern-Simons-type structures and providing a higher-dimensional origin for these theories. The work highlights how duality twists generate new consistent lower-dimensional theories and clarifies the role of duality symmetries in compactifications.

Abstract

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 coupled to supergravity. The reduction cannot be done on the action itself, but must be done either on the field equations or on a duality invariant form of the action, such as one in the doubled formalism in which potentials are introduced for both electric and magnetic fields. The resulting theory in odd-dimensions has massive form fields satisfying a self-duality condition $dA \sim m*A$. We construct such theories in D=3,5,7.