Leibniz Gauge Theories and Infinity Structures

We formulate gauge theories based on Leibniz(-Loday) algebras and uncover their underlying mathematical structure. Various special cases have been developed in the context of gauged supergravity and exceptional field theory. These are based on `tensor hierarchies', which describe towers of $p$-form gauge fields transforming under non-abelian gauge symmetries and which have been constructed up to low levels. Here we define `infinity-enhanced Leibniz algebras' that guarantee the existence of consistent tensor hierarchies to arbitrary level. We contrast these algebras with strongly homotopy Lie algebras ($L_{\infty}$ algebras), which can be used to define topological field theories for which all curvatures vanish. Any infinity-enhanced Leibniz algebra carries an associated $L_{\infty}$ algebra, which we discuss.Comment: 50 pages, v2: refs added, new subsection 3.2, version to appear in Comm. Math. Phy

Perturbative Double Field Theory on General Backgrounds

We develop the perturbation theory of double field theory around arbitrary solutions of its field equations. The exact gauge transformations are written in a manifestly background covariant way and contain at most quadratic terms in the field fluctuations. We expand the generalized curvature scalar to cubic order in fluctuations and thereby determine the cubic action in a manifestly background covariant form. As a first application we specialize this theory to group manifold backgrounds, such as $SU(2) \simeq S^3$ with $H$-flux. In the full string theory this corresponds to a WZW background CFT. Starting from closed string field theory, the cubic action around such backgrounds has been computed before by Blumenhagen, Hassler and L\"ust. We establish precise agreement with the cubic action derived from double field theory. This result confirms that double field theory is applicable to arbitrary curved background solutions, disproving assertions in the literature to the contrary.Comment: 36 pages, v2: minor clarification

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.Comment: 36 pages, v2: refs. added, to appear in JHE

AdS_3/LCFT_2 - Correlators in New Massive Gravity

We calculate 2-point correlators for New Massive Gravity at the chiral point and find that they behave precisely as those of a logarithmic conformal field theory, which is characterized in addition to the central charges c_L = c_R = 0 by `new anomalies' b_L = b_R = -\sigma\frac{12\ell}{G_N}, where \sigma is the sign of the Einstein-Hilbert term, \ell the AdS radius and G_N Newton's constant.Comment: 10 pages, v2: incorrect statement in conclusions deleted, reference added, v3: version to appear in Phys. Lett.

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.Comment: 44 pages, v2: refs. improved, minor corrections, to appear in J. Math. Phy