A bi-invariant Einstein–Hilbert action for the non-geometric string

String and M-theory contain a family of branes forming U -duality multiplets. In particular, standard branes with codimension higher than or equal to two, can be explicitly found as supergravity solutions. However, whether domain-wall branes and space-filling branes can be found as supergravity solutions is still unclear. In this paper, we firstly provide a full list of exotic branes in type II string theory or M-theory compactified to three or higher dimensions. We show how to systematically obtain backgrounds of exotic domain-wall branes and space-filling branes as solutions of the double field theory or the exceptional field theory. Such solutions explicitly depend on the winding coordinates and cannot be given as solutions of the conventional supergravity theories. However, as the domain-wall solutions depend linearly on the winding coordinates, we describe them as solutions of deformed supergravities such as the Romans massive IIA supergravity or lower-dimensional gauged supergravities. We establish explicit relations among the domain-wall branes, the mixed-symmetry potentials, the locally non-geometric fluxes, and deformed supergravities. *

Section: Non-geometric Fluxes and Mixed-symmetry Potentialsmentioning

confidence: 99%

Weaving the exotic web

Fernandez-Melgarejo

Kimura

Sakatani

2018

“…(4.18) does contribute through the classical part of X, Y. Using the torus derivatives: 19) together with the classical part of X, given in eq. (4.14), and that of Y: 20) one obtains the non-trivial contribution to the partition function:…”

Section: T-duality In the Basementioning

confidence: 99%

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

Condeescu

Florakis

Kounnas

et al. 2013

Abstract:We investigate the orbifold limits of string theory compactifications with geometric and non-geometric fluxes. Exploiting the connection between internal fluxes and structure constants of the gaugings in the reduced supergravity theory, we can identify the types of fluxes arising in certain classes of freely-acting symmetric and asymmetric orbifolds. We give a general procedure for deriving the gauge algebra of the effective gauged supergravity using the exact CFT description at the orbifold point. We find that the asymmetry is, in general, related to the presence of non-geometric Q-and R-fluxes. The action of T-duality is studied explicitly on various orbifold models and the resulting transformation of the fluxes is derived. Several explicit examples are provided, including compactifications with geometric fluxes, Q-backgrounds (T-folds) and R-backgrounds. In particular, we present an asymmetric Z 4 × Z 2 orbifold in which all geometric and nongeometric fluxes ω, H, Q, R are turned on simultaneously. We also derive the corresponding flux backgrounds, which are not in general T-dual to geometric ones, and may even simultaneously depend non-trivially on both the coordinates and their winding T-duals.

“…This action for the non-geometric string has recently appeared in the letter [23] of the authors and takes the form…”

Section: Introductionmentioning

confidence: 99%

Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids

Blumenhagen

Deser

Plauschinn

et al. 2013

Self Cite

Based on the structure of a Lie algebroid for non-geometric fluxes in string theory, a differential-geometry calculus is developed which combines usual diffeomorphisms with so-called β-diffeomorphisms emanating from gauge symmetries of the Kalb-Ramond field. This allows to construct a bi-invariant action of Einstein-Hilbert type comprising a metric, a (quasi-)symplectic structure β and a dilaton. As a salient feature, this symplectic gravity action and the resulting equations of motion take a form which is similar to the standard action and field equations. Furthermore, the two actions turn out to be related via a field redefinition reminiscent of the Seiberg-Witten limit. Remarkably, this redefinition admits a direct generalization to higher-order α ′ -corrections and to the additional fields and couplings appearing in the effective action of the superstring. Simple solutions to the equations of motion of the symplectic gravity action, including Calabi-Yau geometries, are discussed.