The gauge algebra of double field theory and Courant brackets

We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the doubled space and transform as vectors under T-duality. The gauge algebra defines a T-duality covariant bracket. For the case in which the parameters and fields are T-dual to ones that have momentum but no winding, we find the gauge transformations to all orders and show that the gauge algebra reduces to one obtained by Siegel. We show that the bracket for such restricted parameters is the Courant bracket. We explain how these algebras are realised as symmetries despite the failure of the Jacobi identity.Comment: 25 pages, LaTe

Service development success: a contingent approach by knowledge strategy

Purpose – Contingency theory suggests that effective strategies and structures are not universal but dependant upon situational factors. The purpose of this paper is to explore how the way service firms compete acts as a strategic contingency, moderating the effect of a new service development (NSD) system on innovation performance. Two knowledge‐based strategies are tested as contingency factors. One strategy adds value for customers via the delivery of personalized knowledge‐based services; the other strategy adds value by services exploiting codified knowledge. Design/methodology/approach – A sample of 70 large service enterprises is used to test a contingency model of service innovation. The NSD system is a synergistic meld of basic building blocks of NSD systems: people organized cross‐functionally, the discipline of formal processes for guiding development activities, and the deployment of enabling tools/technologies. Regression analysis is used to test the relative impact of these three elements on innovation performance contingent on the type of knowledge strategy employed. Findings – While each element of the NSD system has an effect on performance, the optimal design is contingent on the strategy the firm employs. If firms enact a personalization strategy, NSD systems that score high in the deployment of cross‐functional organization and disciplined processes are higher performers. If firms emphasize a codification strategy, NSD systems that score high in the deployment of tools/technologies are higher performers. Combinations of the two kinds of strategy permit the construction of a four‐cell classification of service firms. This typology is used to further explore the implications for how managers design NSD systems to optimize performance. Originality/value – This paper uses a contingency approach to demonstrate that an optimal NSD system is dependent upon the type of knowledge strategy firms deploy. The impact on performance of three components of NSD depends on the degree of either codification and/or personalization in the service offering. A novel approach based on the knowledge management literature is employed creating a typology of service firm strategies. This is the first time such a typology has been postulated

Worldvolume Theories, Holography, Duality and Time

Duality transformations involving compactifications on timelike as well as spacelike circles link M-theory, the 10+1-dimensional strong coupling limit of IIA string theory, to other 11-dimensional theories in signatures 9+2 and 6+5 and to type II string theories in all 10-dimensional signatures. These theories have BPS branes of various world-volume signatures, and here we construct the world-volume theories for these branes, which in each case have 16 supersymmetries. For the generalised D-branes of the various type II string theories, these are always supersymmetric Yang-Mills theories with 16 supersymmetries, and we show that these all arise from compactifications of the supersymmetric Yang-Mills theories in 9+1 or 5+5 dimensions. We discuss the geometry of the brane solutions and, for the cases in which the world-volume theories are superconformally invariant, we propose holographically dual string or M theories in constant curvature backgrounds. For product space solutions $X\times Y$, there is in general a conformal field theory associated with the boundary of $X$ and another with the boundary of $Y$.Comment: 35 pages, harvma

Branes, Times and Dualities

Dualities link M-theory, the 10+1 dimensional strong coupling limit of the IIA string, to other 11-dimensional theories in signatures 9+2 and 6+5, and to type II string theories in all 10-dimensional signatures. We study the Freund-Rubin-type compactifications and brane-type solutions of these theories, and find that branes with various world-volume signatures are possible. For example, the 9+2 dimensional M* theory has membrane-type solutions with world-volumes of signature (3,0) and (1,2), and a solitonic solution with world-volume signature (5,1).Comment: 36 pages, 4 Postscript figures, uses harvmac macr

Generalized Kahler geometry and gerbes

We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahler geometry. The relation between the gerbe and the generalized Kahler potential is discussed.Comment: 28 page

Double Field Theory

The zero modes of closed strings on a torus --the torus coordinates plus dual coordinates conjugate to winding number-- parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be expanded to give an infinite set of fields on the doubled torus. We use the string field theory to construct a theory of massless fields on the doubled torus. Key to the consistency is a constraint on fields and gauge parameters that arises from the L_0 - \bar L_0=0 condition in closed string theory. The symmetry of this double field theory includes usual and 'dual diffeomorphisms', together with a T-duality acting on fields that have explicit dependence on the torus coordinates and the dual coordinates. We find that, along with gravity, a Kalb-Ramond field and a dilaton must be added to support both usual and dual diffeomorphisms. We construct a fully consistent and gauge invariant action on the doubled torus to cubic order in the fields. We discuss the challenges involved in the construction of the full nonlinear theory. We emphasize that the doubled geometry is physical and the dual dimensions should not be viewed as an auxiliary structure or a gauge artifact.Comment: 51 pages. v2: Corrected typo in eqn. (2.48) and very minor typos elsewhere. Added ref. [9] to M. Van Raamsdon

Duality Twists, Orbifolds, and Fluxes

We investigate compactifications with duality twists and their relation to orbifolds and compactifications with fluxes. Inequivalent compactifications are classified by conjugacy classes of the U-duality group and result in gauged supergravities in lower dimensions with nontrivial Scherk-Schwarz potentials on the moduli space. For certain twists, this mechanism is equivalent to introducing internal fluxes but is more general and can be used to stabilize some of the moduli. We show that the potential has stable minima with zero energy precisely at the fixed points of the twist group. In string theory, when the twist belongs to the T-duality group, the theory at the minimum has an exact CFT description as an orbifold. We also discuss more general twists by nonperturbative U-duality transformations.Comment: 30 pages, harvmac, references and brief comments on gauged supergravity adde

Null Brane Intersections

We study pairs of planar D-branes intersecting on null hypersurfaces, and other related configurations. These are supersymmetric and have finite energy density. They provide open-string analogues of the parabolic orbifold and null-fluxbrane backgrounds for closed superstrings. We derive the spectrum of open strings, showing in particular that if the D-branes are shifted in a spectator dimension so that they do not intersect, the open strings joining them have no asymptotic states. As a result, a single non-BPS excitation can in this case catalyze a condensation of massless modes, changing significantly the underlying supersymmetric vacuum state. We argue that a similar phenomenon can modify the null cosmological singularity of the time-dependent orbifolds. This is a stringy mechanism, distinct from black-hole formation and other strong gravitational instabilities, and one that should dominate at weak string coupling. A by-product of our analysis is a new understanding of the appearance of 1/4 BPS threshold bound states, at special points in the moduli space of toroidally-compactified type-II string theory.Comment: Tex file, uses harvmac, 24 pages with 5 figures. Corrected typos and added references. Final version to appear in JHE