arXiv subjects

Falk Hassler

Publications and source records attributed to Falk Hassler.

42 records · Page 3Linked to original sources

arXiv2015

Double Field Theory on Group Manifolds (Thesis)

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 compact group manifold. Its classical action and the corresponding gauge transformations arise from Closed String Field Theory up to cubic order in the massless fields. These results are rewritten in terms of a generalized metric and extended to all orders in the fields. There is an explicit distinction between background and fluctuations. For the gauge algebra to close, the latter have to fulfill a modified strong constraint, while for the former the weaker closure constraint is sufficient. Besides the generalized diffeomorphism invariance known from the original formulation, DFT${}_\mathrm{WZW}$ is invariant under standard diffeomorphisms of the doubled space. They are broken by imposing the totally optional extended strong constraint. In doing so, the original formulation is restored. A flux formulation for the new theory is derived and its connection to generalized Scherk-Schwarz compactifications is discussed. Further, a possible tree-level uplift of a genuinely non-geometric background (not T-dual to any geometric configuration) is presented. Finally, a long standing problem, the missing of a prescription to construct the twist in generalized Scherk-Schwarz compactifications, is solved. Altogether, a more general picture of DFT and the structures it is based on emerges.

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arXiv2015

Generalized Metric Formulation of Double Field Theory on Group Manifolds

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. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFT${}_\mathrm{WZW}$ and of original DFT from tori is clarified. Furthermore we show how to relate DFT${}_\mathrm{WZW}$ of the WZW background with the flux formulation of original DFT.

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arXiv2014

Double Field Theory on Group Manifolds

A new version of double field theory (DFT) is derived for the exactly solvable background of an in general left-right asymmetric WZW model in the large level limit. This generalizes the original DFT that was derived via expanding closed string field theory on a torus up to cubic order. The action and gauge transformations are derived for fluctuations around the generalized group manifold background up to cubic order, revealing the appearance of a generalized Lie derivative and a corresponding C-bracket upon invoking a new version of the strong constraint. In all these quantities a background dependent covariant derivative appears reducing to the partial derivative for a toroidal background. This approach sheds some new light on the conceptual status of DFT, its background (in-)dependence and the up-lift of non-geometric Scherk-Schwarz reductions.

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arXiv2014

Consistent Compactification of Double Field Theory on Non-geometric Flux Backgrounds

In this paper, we construct non-trivial solutions to the $2D$-dimensional field equations of Double Field Theory (DFT) by using a consistent Scherk-Schwarz ansatz. The ansatz identifies $2(D-d)$ internal directions with a twist $U^M{}_N$ which is directly connected to the covariant fluxes $\mathcal{F}_{ABC}$. It exhibits $2(D-d)$ linear independent generalized Killing vectors $K_I{}^J$ and gives rise to a gauged supergravity in $d$ dimensions. We analyze the covariant fluxes and the corresponding gauged supergravity with a Minkowski vacuum. We calculate fluctuations around such vacua and show how they gives rise to massive scalars field and vectors field with a non-abelian gauge algebra. Because DFT is a background independent theory, these fields should directly correspond the string excitations in the corresponding background. For $(D-d)=3$ we perform a complete scan of all allowed covariant fluxes and find two different kinds of backgrounds: the single and the double elliptic case. The later is not T-dual to a geometric background and cannot be transformed to a geometric setting by a field redefinition either. While this background fulfills the strong constraint, it is still consistent with the Killing vectors depending on the coordinates and the winding coordinates, thereby giving a non-geometric patching. This background can therefore not be described in Supergravity or Generalized Geometry.

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arXiv2014

Non-associative Deformations of Geometry in Double Field Theory

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.

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arXiv2013

Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections

In this paper we discuss the construction of non-geometric Q- and R-branes as sources of non-geometric Q- and R-fluxes in string compactifications. The non-geometric Q-branes, being obtained via T-duality from the NS 5-brane or respectively from the KK-monopole, are still local solutions of the standard NS action, where however the background fields G and B possess non-geometric global monodromy properties. We show that using double field theory, redefined background fields tilde G and beta as well as their corresponding effective action, the Q-branes are locally and globally well behaved solutions. Furthermore the R-brane solution can be at least formally constructed using dual coordinates. We derive the associated non-geometric Q- and R-fluxes and discuss that closed strings moving in the space transversal to the world-volumes of the non-geometric branes see a non-commutative or a non-associative geometry. In the second part of the paper we construct intersecting Q- and R-brane configurations as completely supersymmetric solutions of type IIA/B supergravity with certain SU(3) x SU(3) group structures. In the near horizon limit the intersecting brane configurations lead to type II backgrounds of the form AdS4 x M6, where the six-dimensional compact space M6 is a torus fibration with various non-geometric Q- and R-fluxes in the compact directions. It exhibits an interesting non-commutative and non-associate geometric structure. Furthermore we also determine some of the effective four-dimensional superpotentials originating from the non-geometric fluxes.

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