We develop the formulation of DFT on pre-QP-manifold. The consistency conditions like section condition and closure constraint are unified by a weak master equation. The Bianchi identities are also characterized by the pre-Bianchi identity. Then, the background metric and connections are formulated by using covariantized pre-QP-manifold. An application to the analysis of the DFT on group manifold is given.
We generalize the formulation of Poisson-Lie T-dual sigma models on manifolds to supermanifolds. In this respect, we formulate 1+1 dimensional string cosmological models on the Lie supergroup C^3 and its dual (A_1,1 + 2A)^0_(1,0,0), which are coupled to two fermionic fields. Then, we solve the equations of motion of the models and show that there is a essential singularity for the metric of the original model and its dual.
Over many decades, the word "double" has appeared in various contexts, at times seemingly unrelated. Several have some relation to mathematical physics. Recently, this has become particularly strking in DFT (double field theory). Two 'doubles' that are particularly relevant are double vector bundles and Drinfel'd doubles. The original Drinfel'd double occurred in the contexts of quantum groups and of Lie bialgebras. Quoting T. Voronov: "Double Lie algebroids arose in the works on double Lie groupoids and in connection with an analog for Lie bialgebroids of the classical Drinfel'd double of Lie…
We rewrite the recently derived cubic action of Double Field Theory on group manifolds [arXiv:1410.6374] in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized diffeomorphisms and 2D-diffeomorphisms.…
A flux formulation of Double Field Theory on group manifold is derived and applied to study generalized Scherk-Schwarz compactifications, which give rise to a bosonic subsector of half-maximal, electrically gauged supergravities. In contrast to the flux formulation of original DFT, the covariant fluxes split into a fluctuation and a background part. The latter is connected to a $2D$-dimensional, pseudo Riemannian manifold, which is isomorphic to a Lie group embedded into O($D,D$). All fields and parameters of generalized diffeomorphisms are supported on this manifold, whose metric is spanned b…
We present a formulation of heterotic Double Field Theory (DFT), where the fundamental fields are in $O(D,D)$ representations. The theory is obtained splitting an $O(D,D+K)$ duality invariant DFT. This procedure produces a Green-Schwarz mechanism for the generalized metric, and a fundamental gauge field which transforms as a gauge connection only to leading order. After parametrization, the former induces a non-covariant transformation on the metric tensor, which can be removed considering field redefinitions, and an ordinary Green-Schwarz mechanism on the b-field. Within this framework we exp…
This thesis deals with new backgrounds and concepts in Double Field Theory (DFT), a T-Duality invariant reformulation of supergravity (SUGRA). We begin by reviewing the basic concepts and notions of DFT. Afterwards, we turn to Double Field Theory on group manifolds (DFT$_{\mathrm{WZW}}$). In order to obtain its action and gauge transformations, Closed String Field Theory (CSFT) computations are performed on a worldsheet, governed by a Wess-Zumino-Witten model on a group manifold. We consider generalized diffeomorphisms and their gauge algebra, which closes under a modified strong constraint. T…
Double field theory (DFT) offers a manifest T-duality formulation for massless closed string field theory with both momentum and winding excitation. The gauge symmetry is defined by the generalized Lie derivative which is the extension of the Courant bracket. In this work, we solve and study the properties of FRW (Friedmann- Robertson-Walker) and doubled spherically symmetric metric of DFT.
This thesis deals with Double Field Theory (DFT), an effective field theory capturing the low energy dynamics of closed strings on a torus. It renders T-duality on a torus manifest by adding $D$ winding coordinates in addition to the $D$ space time coordinates. An essential consistency constraint of the theory, the strong constraint, only allows for field configurations which depend on half of the coordinates of the arising doubled space. I derive DFT${}_\mathrm{WZW}$, a generalization of the current formalism. It captures the low energy dynamics of a closed bosonic string propagating on a com…
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）；Ludwig Maximilian University（慕尼黑大学）；Universitá degli Studi di Bari ‘Aldo Moro’（巴里阿尔多·莫罗大学）
We present a new formulation of curved projective superspace. The 4D N=2 supermanifold M^{4|8} (four bosonic and eight Grassmann coordinates) is extended by an auxiliary SU(2) manifold, which involves introducing a vielbein and related connections on the full M^{7|8} = M^{4|8} x SU(2). Constraints are chosen so that it is always possible to return to the central gauge where the auxiliary SU(2) manifold largely decouples from the curved manifold M^{4|8} describing 4D N=2 conformal supergravity. We introduce the relevant projective superspace action principle in the analytic subspace of M^{7|8} …
In this sequel to works D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we re-examine --- and reformulate when in need --- several basic notions in super $C^{\infty}$-algebraic geometry as guided by the mathematical formulation of Ramond-Neveu-Schwarz fermionic strings and of Green-Schwarz fermionic strings from the viewpoint of Grothendieck on Algebraic Geometry. Two theorems that are the super counterpart of Theorem~3.1.1 and Theorem~3.2.1 of D(11.3.1) are proved. They unify the notion of "smooth maps from an Azumaya/matrix…
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…
We give a formulation of Double Field Theory (DFT) based on a metric algebroid. We derive a covariant completion of the Bianchi identities, i.e. the pre-Bianchi identity in torsion and an improved generalized curvature, and the pre-Bianchi identity including the dilaton contribution. The derived bracket formulation by the Dirac generating operator is applied to the metric algebroid. We propose a generalized Lichnerowicz formula and show that it is equivalent to the pre-Bianchi identities. The dilaton in this setting is included as an ambiguity in the divergence. The projected generalized Lichn…
Non-geometric string backgrounds were proposed to be related to a non-associative deformation of the space-time geometry. In the flux formulation of double field theory (DFT), the structure of mathematically possible non-associative deformations is analyzed in detail. It is argued that on-shell there should not be any violation of associativity in the effective DFT action. For imposing either the strong or the weaker closure constraint we discuss two possible non-associative deformations of DFT featuring two different ways how on-shell associativity can still be kept.
Originally proposed as an $O(d,d)$-invariant formulation of classical closed string theory, double field theory (DFT) offers a rich source of mathematical structures. Most prominently, its gauge algebra is determined by the so-called C-bracket, a generalization of the Courant bracket of generalized geometry, in the sense that it reduces to the latter by restricting the theory to solutions of a "strong constraint". Recently, infinitesimal deformations of these structures in the string sigma model coupling $α'$ were found. In this short contribution, we review constructing the Drinfel'd double o…
We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and without 1-, 2- and 3-form gauge potentials as well as DFT. We believe that our extended Riemannian geometry helps to clarify the role of various constructions in DFT. For example, it leads to a covariant form of the strong section condition. Furthermore, it should provide a useful st…
We continue our exploration of local Double Field Theory (DFT) in terms of symplectic graded manifolds carrying compatible derivations and study the case of heterotic DFT. We start by developing in detail the differential graded manifold that captures heterotic Generalized Geometry which leads to new observations on the generalized metric and its twists. We then give a symplectic pre-NQ-manifold that captures the symmetries and the geometry of local heterotic DFT. We derive a weakened form of the section condition, which arises algebraically from consistency of the symmetry Lie 2-algebra and i…
We present the first successful functional renormalization group(FRG)-aided density-functional (DFT) calculation of the equation of state (EOS) of an infinite nuclear matter (NM) in (1+1)-dimensions composed of spinless nucleons. We give a formulation to describe infinite matters in which the 'flowing' chemical potential is introduced to control the particle number during the flow. The resultant saturation energy of the NM coincides with that obtained by the Monte-Carlo method within a few percent. Our result demonstrates that the FRG-aided DFT can be as powerful as any other methods in quantu…
