Generalized 11D supergravity equations from tri-vector deformations

In arXiv:2203.03372 we presented a modification of 11-dimensional supergravity field equations which upon dimensional reduction yields generalized supergravity equations in 10-dimensions. In this paper we provide full technical details of that result which is based on SL(5) exceptional field theory. The equations are obtained by making a non-unimodular tri-vector Yang-Baxter deformation which breaks the initial GL(11) symmetry down to GL(7)xGL(4). We also give some non-trivial solutions to these equations.Comment: v3, refs added, minor correction

Duality Twists on a Group Manifold

We study duality-twisted dimensional reductions on a group manifold G, where the twist is in a group \tilde{G} and examine the conditions for consistency. We find that if the duality twist is introduced through a group element \tilde{g} in \tilde{G}, then the flat \tilde{G}-connection A =\tilde{g}^{-1} d\tilde{g} 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,R) twist.Comment: 22 page

Beta, Dipole and Noncommutative Deformations of M-theory Backgrounds with One or More Parameters

We construct new M-theory solutions starting from those that contain 5 U(1) isometries. We do this by reducing along one of the 5-torus directions, then T-dualizing via the action of an O(4,4) matrix and lifting back to 11-dimensions. The particular T-duality transformation is a sequence of O(2,2) transformations embedded in O(4,4), where the action of each O(2,2) gives a Lunin-Maldacena deformation in 10-dimensions. We find general formulas for the metric and 4-form field of single and multiparameter deformed solutions, when the 4-form of the initial 11-dimensional background has at most one leg along the 5-torus. All the deformation terms in the new solutions are given in terms of subdeterminants of a 5x5 matrix, which represents the metric on the 5-torus. We apply these results to several M-theory backgrounds of the type AdS_r x X^{11-r}. By appropriate choices of the T-duality and reduction directions we obtain analogues of beta, dipole and noncommutative deformations. We also provide formulas for backgrounds with only 3 or 4 U(1) isometries and study a case, for which our assumption for the 4-form field is violated.Comment: v2:minor corrections, v3:small improvements, v4:conclusions expanded, to appear in Class. Quant. Gra

A Massive S-duality in 4 dimensions

We reduce the Type IIA supergravity theory with a generalized Scherk-Schwarz ansatz that exploits the scaling symmetry of the dilaton, the metric and the NS 2-form field. The resulting theory is a new massive, gauged supergravity theory in four dimensions with a massive 2-form field and a massive 1-form field. We show that this theory is S-dual to a theory with a massive vector field and a massive 2-form field, which are dual to the massive 2-form and 1-form fields in the original theory, respectively. The S-dual theory is shown to arise from a Scherk-Schwarz reduction of the heterotic theory. Hence we establish a massive, S-duality type relation between the IIA theory and the heterotic theory in four dimensions. We also show that the Lagrangian for the new four dimensional theory can be put in the most general form of a D=4, N=4 gauged Lagrangian found by Schon and Weidner, in which (part of) the SL(2) group has been gauged.Comment: 20 pages, references adde

Çift sayıda boyuta sahip uzaylarda efektif sicim kuramlarının Scherk-Schwarz indirgemesi

Scherk-Schwarz reductions are a generalization of Kaluza-Klein reductions in which the higher dimensional fields are allowed to have a dependence on the compactiifed coordinates. This is possible only if the higher dimensional theory has a global symmetry and the dependence is dictated by this symmetry. In this thesis 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 ÞD=4, N=4Þ 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 ÞdAPh.D. - Doctoral Progra