Duality twists on a group manifold

Abstract

We study duality-twisted dimensional reductions on a group manifold G, where the twist is in a groupG and examine the conditions for consistency. We find that if the duality twist is introduced through a group elementg inG, then the flatG-connection A =g −1 dg must have constant components M n with respect to the basis 1-forms on G, so that the dependence on the internal coordinates cancels out in the lower dimensional theory. This condition can be satisfied if and only if M n forms a representation of the Lie algebra of G, which then ensures that the lower dimensional gauge algebra closes. We find the form of this gauge algebra and compare it to that arising from flux compactifications on twisted tori. As an example of our construction, we find a new five dimensional gauged, massive supergravity theory by dimensionally reducing the eight dimensional Type II supergravity on a three dimensional unimodular, non-semi-simple, non-abelian group manifold with an SL(3, IR) twist.

S-folds and 4d N $$ \mathcal{N} $$ = 3 superconformal field theories

“…This term, first coined in[8], generalizes the term T-folds that is used to describe identifications by elements of the T-duality group. S-folds of string theory involving S-duality twists together with shifts along a circle were studied, for instance, in[9,10,11,12,13], and similar S-folds were studied in the 4d N = 4 SYM theory in[14,15,16].…”

O(d,d) covariant formulation of Type II supergravity and Scherk-Schwarz reduction

“…The lower dimensional theory has an SL(2, R) symmetry as part of its global symmetry group, as SL(2, R) is the large diffeomorphism group of T 2 . In a further compactification on a circle S 1 one can introduce a duality-twisted ansatz for these fields as in (31), where U (y) is in SL(2, R) [51,52,53,54,55]. The total 3 dimensional internal space is usually called a twisted torus in the literature.…”

Cosmology with twisted tori

“…These groups [10] are related to the ISO(N) group of isometries in N -dimensional space, and are described by the structure constants f a bc , where the indices a, b, c = 0, 1, 2... and the non-zero components are given by…”

“…These manifolds are related to the duality twists of [7,10], where they are identified as elliptic twisted tori and related to the Lie group ISO(N ). Two further groups which should fulfil the needs of our model are also presented there, the hyperbolic and parabolic classes, respectively related to the Lie group SO(P, Q) and the Heisenberg group.…”