T‐duality, Quotients and Currents for Non‐Geometric Closed Strings

We investigate geometric aspects of double field theory (DFT) and its formulation as a doubled membrane sigma-model. Starting from the standard Courant algebroid over the phase space of an open membrane, we determine a splitting and a projection to a subbundle that sends the Courant algebroid operations to the corresponding operations in DFT. This describes precisely how the geometric structure of DFT lies in between two Courant algebroids and is reconciled with generalized geometry. We construct the membrane sigma-model that corresponds to DFT, and demonstrate how the standard T-duality orbit of geometric and non-geometric flux backgrounds is captured by its action functional in a unified way. This also clarifies the appearence of noncommutative and nonassociative deformations of geometry in non-geometric closed string theory. Gauge invariance of the DFT membrane sigma-model is compatible with the flux formulation of DFT and its strong constraint, whose geometric origin is explained. Our approach leads to a new generalization of a Courant algebroid, that we call a DFT algebroid and relate to other known generalizations, such as pre-Courant algebroids and symplectic nearly Lie 2-algebroids. We also describe the construction of a gauge-invariant doubled membrane sigma-model that does not require imposing the strong constraint. 1 a.chatzistavrakidis@gmail.com 2 larisa@irb.hr 3 Fech.Scen.Khoo@irb.hr 4 R.J.Szabo@hw.ac.uk 29)19 In this subsection we simplify the notation for the components of the map ρ + by denoting (ρ + ) I J as ρ I J .

Section: Locally Non-geometric Flux and Nonassociativitymentioning

confidence: 99%

Double field theory and membrane sigma-models

Chatzistavrakidis

Jonke

Khoo

et al. 2018

“…Deformations of spacetime geometry through compactifications of string theory may help elucidate the precise mechanism by which closed strings provide a framework for a quantum theory of gravity. This has been the hope in some recent investigations surrounding non-geometric string theory, in which noncommutative and nonassociative deformations of target space geometry have been purported to be probed by closed strings in non-geometric flux compactifications [15,25,16,19,1,17,13,9]. In particular, in locally non-geometric backgrounds one aims to find a low-energy limit of closed string theory which is described by an effective nonassociative theory of gravity on spacetime.…”

Section: Introductionmentioning

confidence: 99%

Nonassociative differential geometry and gravity with non-geometric fluxes

Aschieri

Ćirić

Szabo

2018

164

We systematically develop the metric aspects of nonassociative differential geometry tailored to the parabolic phase space model of constant locally non-geometric closed string vacua, and use it to construct preliminary steps towards a nonassociative theory of gravity on spacetime. We obtain explicit expressions for the torsion, curvature, Ricci tensor and Levi-Civita connection in nonassociative Riemannian geometry on phase space, and write down Einstein field equations. We apply this formalism to construct R-flux corrections to the Ricci tensor on spacetime, and comment on the potential implications of these structures in non-geometric string theory and double field theory.

“…In the cases we examined we found a mixing of the original coordinates and the would-be dual coordinates, which is indicative of doubled formulations, such as the doubled sigma models considered by Hull [32] or the ones recently studied in [33]. Last but not least, it would be very interesting to apply this formalism in the case of the triple T-dual of a torus with H flux, or equivalently to the T-dual of the Q flux background where no isometry is available (recent attempts to understand this problem include [34][35][36]), and even more so in cases of true string backgrounds. We will report on these and other issues in future publications.…”

Section: Jhep01(2016)154mentioning

confidence: 99%

T-duality without isometry via extended gauge symmetries of 2D sigma models

Chatzistavrakidis

Deser

Jonke

2016

Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail the possibility to perform T-duality along non-isometric directions. In particular, based on a recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge invariance for an extended set of gauge transformations imposes weaker constraints than in the standard case, notably the corresponding vector fields are not Killing. This formulation enables us to follow a procedure analogous to the derivation of the Buscher rules and obtain two dual models, by integrating out once the Lagrange multipliers and once the gauge fields. We show that this construction indeed works in non-trivial cases by examining an explicit class of examples based on step 2 nilmanifolds.