Quantum Mechanics of the Doubled Torus

We investigate the quantum mechanics of the doubled torus system, introduced by Hull [1] to describe T-folds in a more geometric way. Classically, this system consists of a world-sheet Lagrangian together with some constraints, which reduce the number of degrees of freedom to the correct physical number. We consider this system from the point of view of constrained Hamiltonian dynamics. In this case the constraints are second class, and we can quantize on the constrained surface using Dirac brackets. We perform the quantization for a simple T-fold background and compare to results for the conventional non-doubled torus system. Finally, we formulate a consistent supersymmetric version of the doubled torus system, including supersymmetric constraints.Comment: 31 pages, 1 figure; v2: references added, minor corrections to final sectio

Superstring partition functions in the doubled formalism

Computation of superstring partition function for the non-linear sigma model on the product of a two-torus and its dual within the scope of the doubled formalism is presented. We verify that it reproduces the partition functions of the toroidally compactified type--IIA and type--IIB theories for appropriate choices of the GSO projection.Comment: 15 page

Generalised Geometry for M-Theory

Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge field on which there is a natural action of the group $E_{d}$. This provides a framework for the discussion of M-theory solutions with flux. A different generalisation is to d-dimensional manifolds with a metric, 2-form gauge field and a set of p-forms for $p$ either odd or even on which there is a natural action of the group $E_{d+1}$. This is useful for type IIA or IIB string solutions with flux. Further generalisations give extended tangent bundles and extended spin bundles relevant for non-geometric backgrounds. Special structures that arise for supersymmetric backgrounds are discussed.Comment: 31 page

D-branes in T-fold conformal field theory

We investigate boundary dynamics of orbifold conformal field theory involving T-duality twists. Such models typically appear in contexts of non-geometric string compactifications that are called monodrofolds or T-folds in recent literature. We use the framework of boundary conformal field theory to analyse the models from a microscopic world-sheet perspective. In these backgrounds there are two kinds of D-branes that are analogous to bulk and fractional branes in standard orbifold models. The bulk D-branes in T-folds allow intuitive geometrical interpretations and are consistent with the classical analysis based on the doubled torus formalism. The fractional branes, on the other hand, are `non-geometric' at any point in the moduli space and their geometric counterparts seem to be missing in the doubled torus analysis. We compute cylinder amplitudes between the bulk and fractional branes, and find that the lightest modes of the open string spectra show intriguing non-linear dependence on the moduli (location of the brane or value of the Wilson line), suggesting that the physics of T-folds, when D-branes are involved, could deviate from geometric backgrounds even at low energies. We also extend our analysis to the models with SU(2) WZW fibre at arbitrary levels.Comment: 38 pages, no figure, ams packages. Essentially the published versio

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

Generalized Flux Vacua

We consider type II string theory compactified on a symmetric T^6/Z_2 orientifold. We study a general class of discrete deformations of the resulting four-dimensional supergravity theory, including gaugings arising from geometric and "nongeometric'' fluxes, as well as the usual R-R and NS-NS fluxes. Solving the equations of motion associated with the resulting N = 1 superpotential, we find parametrically controllable infinite families of supersymmetric vacua with all moduli stabilized. We also describe some aspects of the distribution of generic solutions to the SUSY equations of motion for this model, and note in particular the existence of an apparently infinite number of solutions in a finite range of the parameter space of the four-dimensional effective theory.Comment: 30 pages, 4 .eps figures; v2, reference adde

Mirrorfolds with K3 Fibrations

We study a class of non-geometric string vacua realized as completely soluble superconformal field theory (SCFT). These models are defined as `interpolating orbifolds' of $K3 \times S^1$ by the mirror transformation acting on the $K3$ fiber combined with the half-shift on the $S^1$-base. They are variants of the T-folds, the interpolating orbifolds by T-duality transformations, and thus may be called `mirrorfolds'. Starting with arbitrary (compact or non-compact) Gepner models for the $K3$ fiber, we construct modular invariant partition functions of general mirrorfold models. In the case of compact $K3$ fiber the mirrorfolds only yield non-supersymmetric string vacua. They exhibit IR instability due to winding tachyon condensation which is similar to the Scherk-Schwarz type circle compactification. When the fiber SCFT is non-compact (say, the ALE space in the simplest case), on the other hand, both supersymmetric and non-supersymmetric vacua can be constructed. The non-compact non-supersymmetric mirrorfolds can get stabilised at the level of string perturbation theory. We also find that in the non-compact supersymmeric mirrorfolds D-branes are {\em always} non-BPS. These D-branes can get stabilized against both open- and closed-string marginal deformations.Comment: Eqns (2.61) and (3.17) correcte

On BPS preons, generalized holonomies and D=11 supergravities

We develop the BPS preon conjecture to analyze the supersymmetric solutions of D=11 supergravity. By relating the notions of Killing spinors and BPS preons, we develop a moving G-frame method (G=GL(32,R), SL(32,R) or Sp(32,R)) to analyze their associated generalized holonomies. As a first application we derive here the equations determining the generalized holonomies of k/32 supersymmetric solutions and, in particular, those solving the necessary conditions for the existence of BPS preonic (31/32) solutions of the standard D=11 supergravity. We also show that there exist elementary preonic solutions, i.e. solutions preserving 31 out of 32 supersymmetries in a Chern--Simons type supergravity. We present as well a family of worldvolume actions describing the motion of pointlike and extended BPS preons in the background of a D'Auria-Fre type OSp(1|32)-related supergravity model. We discuss the possible implications for M-theory.Comment: 11 pages, RevTeX Typos corrected, a short note and references adde

Supersymmetric string model with 30 kappa--symmetries in an extended D=11 superspace and 30/ 32 BPS states

A supersymmetric string model in the D=11 superspace maximally extended by antisymmetric tensor bosonic coordinates, $\Sigma^{(528|32)}$, is proposed. It possesses 30 $\kappa$-symmetries and 32 target space supersymmetries. The usual preserved supersymmetry-$\kappa$-symmetry correspondence suggests that it describes the excitations of a BPS state preserving all but two supersymmetries. The model can also be formulated in any $\Sigma^{({n(n+1)\over 2}|n)}$ superspace, n=32 corresponding to D=11. It may also be treated as a `higher--spin generalization' of the usual Green--Schwarz superstring. Although the global symmetry of the model is a generalization of the super--Poincar\'e group, ${\Sigma}^{({n(n+1)\over 2}|n)}\times\supset Sp(n)$, it may be formulated in terms of constrained OSp(2n|1) orthosymplectic supertwistors. We work out this supertwistor realization and its Hamiltonian dynamics. We also give the supersymmetric p-brane generalization of the model. In particular, the $\Sigma^{(528|32)}$ supersymmetric membrane model describes excitations of a 30/32 BPS state, as the $\Sigma^{(528|32)}$ supersymmetric string does, while the supersymmetric 3-brane and 5-brane correspond, respectively, to 28/32 and 24/32 BPS states.Comment: 23 pages, RevTex4. V2: minor corrections in title and terminology, some references and comments adde