arXiv subjects

Olaf Hohm

Publications and source records attributed to Olaf Hohm.

At least 91 records · Page 5Linked to original sources

arXiv2013

Zwei-Dreibein Gravity

We present a generally-covariant and parity-invariant "zwei-dreibein" action for gravity in three space-time dimensions that propagates two massive spin-2 modes, unitarily, and we use Hamiltonian methods to confirm the absence of unphysical degrees of freedom. We show how zwei-dreibein gravity unifies previous "3D massive gravity" models, and extends them, in the context of the AdS/CFT correspondence, to allow for a positive central charge consistent with bulk unitarity.

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arXiv2013

Exceptional Form of D=11 Supergravity

Eleven-dimensional supergravity reveals large exceptional symmetries upon reduction, in accordance with the U-duality groups of M-theory, but their higher-dimensional geometric origin has remained a mystery. In this letter, we show that D=11 supergravity can be extended to be fully covariant under the exceptional groups E_{n(n)}, n=6,7,8. Motivated by a similar formulation of double field theory we introduce an extended `exceptional spacetime'. We illustrate the construction by giving the explicit E_{6(6)} covariant form: the full D=11 supergravity, in a 5+6 splitting of coordinates but without truncation, embeds into an E_{6(6)} covariant 5+27 dimensional theory. We argue that this covariant form likewise comprises type IIB supergravity.

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arXiv2013

Gauge theory of Kaluza-Klein and winding modes

We perform a Kaluza-Klein inspired rewriting of double field theory by splitting the coordinates into `compact' and `non-compact' directions. There is no truncation of the compact coordinates or their duals, and so this formulation is manifestly O(d,d) invariant, with d the number of compact directions. The action can serve as starting point for arbitrary Kaluza-Klein ansaetze. For a torus background the theory describes the full tower of Kaluza-Klein modes or, in the dual frame, of the winding modes. The Kaluza-Klein vector is a gauge field for the duality-covariantized Courant bracket algebra rather than a Lie algebra. Gauge covariance requires the inclusion of the 2-form gauge potential descending from the Kalb-Ramond field, leading to a structure resembling the tensor hierarchy of gauged supergravity.

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arXiv2013

U-duality covariant gravity

We extend the techniques of double field theory to more general gravity theories and U-duality symmetries, having in mind applications to the complete D=11 supergravity. In this paper we work out a (3+3)-dimensional `U-duality covariantization' of D=4 Einstein gravity, in which the Ehlers group SL(2,R) is realized geometrically, acting in the 3 representation on half of the coordinates. We include the full (2+1)-dimensional metric, while the `internal vielbein' is a coset representative of SL(2,R)/SO(2) and transforms under gauge transformations via generalized Lie derivatives. In addition, we introduce a gauge connection of the `C-bracket', and a gauge connection of SL(2,R), albeit subject to constraints. The action takes the form of (2+1)-dimensional gravity coupled to a Chern-Simons-matter theory but encodes the complete D=4 Einstein gravity. We comment on generalizations, such as an `$E_{8(8)}$ covariantization' of M-theory.

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arXiv2013

Towards an invariant geometry of double field theory

We introduce a geometrical framework for double field theory in which generalized Riemann and torsion tensors are defined without reference to a particular basis. This invariant geometry provides a unifying framework for the frame-like and metric-like formulations developed before. We discuss the relation to generalized geometry and give an `index-free' proof of the algebraic Bianchi identity. Finally, we analyze to what extent the generalized Riemann tensor encodes the curvatures of Riemannian geometry. We show that it contains the conventional Ricci tensor and scalar curvature but not the full Riemann tensor, suggesting the possibility of a further extension of this framework.

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arXiv2013

Large Gauge Transformations in Double Field Theory

Finite gauge transformations in double field theory can be defined by the exponential of generalized Lie derivatives. We interpret these transformations as `generalized coordinate transformations' in the doubled space by proposing and testing a formula that writes large transformations in terms of derivatives of the coordinate maps. Successive generalized coordinate transformations give a generalized coordinate transformation that differs from the direct composition of the original two. Instead, it is constructed using the Courant bracket. These transformations form a group when acting on fields but, intriguingly, do not associate when acting on coordinates.

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arXiv2012

On the Hamiltonian form of 3D massive gravity

We present a "Chern-Simons-like" action for the "general massive gravity" model propagating two spin-2 modes with independent masses in three spacetime dimensions (3D), and we use it to find a simple Hamiltonian form of this model. The number of local degrees of freedom, determined by the dimension of the physical phase space, agrees with a linearized analysis except in some limits, in particular that yielding "new topologically massive gravity", which therefore suffers from a linearization instability.

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arXiv2012

On the Riemann Tensor in Double Field Theory

Double field theory provides T-duality covariant generalized tensors that are natural extensions of the scalar and Ricci curvatures of Riemannian geometry. We search for a similar extension of the Riemann curvature tensor by developing a geometry based on the generalized metric and the dilaton. We find a duality covariant Riemann tensor whose contractions give the Ricci and scalar curvatures, but that is not fully determined in terms of the physical fields. This suggests that α' corrections to the effective action require α' corrections to T-duality transformations and/or generalized diffeomorphisms. Further evidence to this effect is found by an additional computation that shows that there is no T-duality invariant four-derivative object built from the generalized metric and the dilaton that reduces to the square of the Riemann tensor.

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arXiv2012

A geometric action for non-geometric fluxes

We give a geometrical interpretation of the non-geometric Q and R fluxes. To this end we consider double field theory in a formulation that is related to the conventional one by a field redefinition taking the form of a T-duality inversion. The R flux is a tensor under diffeomorphisms and satisfies a non-trivial Bianchi identity. The Q flux can be viewed as part of a connection that covariantizes the winding derivatives with respect to diffeomorphisms. We give a higher-dimensional action with a kinetic term for the R flux and a 'dual' Einstein-Hilbert term containing the connection Q.

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arXiv2012

Non-linear parent action and dual gravity

We give a reformulation of non-linear Einstein gravity, which contains the dual graviton together with the ordinary metric and a shift gauge field. The metric does not enter through a `kinetic' Einstein-Hilbert term, but via topological couplings, and so the theory does not lead to a doubling of degrees of freedom. The field equations take the form of first-order duality relations. We analyze the gauge symmetries and comment on their meaning with regard to the E11 proposal.

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arXiv2012

Non-Geometric Fluxes in Supergravity and Double Field Theory

In this paper we propose ten-dimensional realizations of the non-geometric fluxes Q and R. In particular, they appear in the NSNS Lagrangian after performing a field redefinition that takes the form of a T-duality transformation. Double field theory simplifies the computation of the field redefinition significantly, and also completes the higher-dimensional picture by providing a geometrical role for the non-geometric fluxes once the winding derivatives are taken into account. The relation to four-dimensional gauged supergravities, together with the global obstructions of non-geometry, are discussed.

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arXiv2012

N=1 Supersymmetric Double Field Theory

We construct the N=1 supersymmetric extension of double field theory for D=10, including the coupling to an arbitrary number n of abelian vector multiplets. This theory features a local O(1,9+n) x O(1,9) tangent space symmetry under which the fermions transform. It is shown that the supersymmetry transformations close into the generalized diffeomorphisms of double field theory.

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arXiv2011

Unification of Type II Strings and T-duality

We present a unified description of the low-energy limits of type II string theories. This is achieved by a formulation that doubles the space-time coordinates in order to realize the T-duality group O(10,10) geometrically. The Ramond-Ramond fields are described by a spinor of O(10,10), which couples to the gravitational fields via the Spin(10,10) representative of the so-called generalized metric. This theory, which is supplemented by a T-duality covariant self-duality constraint, unifies the type II theories in that each of them is obtained for a particular subspace of the doubled space.

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arXiv2011

Double Field Theory of Type II Strings

We use double field theory to give a unified description of the low energy limits of type IIA and type IIB superstrings. The Ramond-Ramond potentials fit into spinor representations of the duality group O(D,D) and field-strengths are obtained by acting with the Dirac operator on the potentials. The action, supplemented by a Spin^+(D,D)-covariant self-duality condition on field strengths, reduces to the IIA and IIB theories in different frames. As usual, the NS-NS gravitational variables are described through the generalized metric. Our work suggests that the fundamental gravitational variable is a hermitian element of the group Spin(D,D) whose natural projection to O(D,D) gives the generalized metric.

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arXiv2011

Massive Type II in Double Field Theory

We provide an extension of the recently constructed double field theory formulation of the low-energy limits of type II strings, in which the RR fields can depend simultaneously on the 10-dimensional space-time coordinates and linearly on the dual winding coordinates. For the special case that only the RR one-form of type IIA carries such a dependence, we obtain the massive deformation of type IIA supergravity due to Romans. For T-dual configurations we obtain a `massive' but non-covariant formulation of type IIB, in which the 10-dimensional diffeomorphism symmetry is deformed by the mass parameter.

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arXiv2011

Double Field Theory Formulation of Heterotic Strings

We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under O(D,D+n), where n denotes the number of gauge vectors, and n additional coordinates are introduced together with a covariant constraint that locally removes these new coordinates. For the abelian subsector, the action takes the same structural form as for the bosonic string, but based on the enlarged generalized metric, thereby featuring a global O(D,D+n) symmetry. After turning on non-abelian gauge couplings, this global symmetry is broken, but the action can still be written in a fully O(D,D+n) covariant fashion, in analogy to similar constructions in gauged supergravities.

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arXiv2011

On factorizations in perturbative quantum gravity

Some features of Einstein gravity are most easily understood from string theory but are not manifest at the level of the usual Lagrangian formulation. One example is the factorization of gravity amplitudes into gauge theory amplitudes. Based on the recently constructed `double field theory' and a geometrical frame-like formalism developed by Siegel, we provide a framework of perturbative Einstein gravity coupled to a 2-form and a dilaton in which, as a consequence of T-duality, the Feynman rules factorize to all orders in perturbation theory. We thereby establish the precise relation between the field variables in different formulations and discuss the Lagrangian that, when written in terms of these variables, makes a left-right factorization manifest.

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arXiv2011

Modes of Log Gravity

The physical modes of a recently proposed D-dimensional "critical gravity", linearized about its anti-de Sitter vacuum, are investigated. All "log mode" solutions, which we categorize as `spin 2' or `Proca', arise as limits of the massive spin 2 modes of the non-critical theory. The linearized Einstein tensor of a spin 2 log mode is itself a 'non-gauge' solution of the linearized Einstein equations whereas the linearized Einstein tensor of a Proca mode takes the form of a linearized general coordinate transformation. Our results suggest the existence of a holographically dual logarithmic conformal field theory.

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