Ronald A. Reid-Edwards

Non-geometric backgrounds, doubled geometry and generalised T-duality

String backgrounds with a local torus fibration such as T-folds are naturally formulated in a doubled formalism in which the torus fibres are doubled to include dual coordinates conjugate to winding number. Here we formulate and explore a generalisation of this construction in which all coordinates are doubled, so that the doubled space is a twisted torus, i.e. a compact space constructed from identifying a group manifold under a discrete subgroup. This incorporates reductions with duality twists, T-folds and a class of flux compactifications, together with the non-geometric backgrounds expected to arise from these through T-duality. It also incorporates backgrounds that are not even locally geometric, and suggests a generalisation of T-duality to a more general context. We discuss the effective field theory arising from such an internal sector, give a world-sheet sigma model formulation of string theory on such backgrounds and illustrate our discussion with detailed examples.

D-branes and doubled geometry

We define the open string version of the nonlinear sigma model on doubled geometry introduced by Hull and Reid-Edwards, and derive its boundary conditions. These conditions include the restriction of D-branes to maximally isotropic submanifolds as well as a compatibility condition with the Lie algebra structure on the doubled space. We demonstrate a systematic method to derive and classify D-branes from the boundary conditions, in terms of embeddings both in the doubled geometry and in the physical target space. We apply it to the doubled three-torus with constant H-flux and find D0-, D1-, and D2-branes, which we verify transform consistently under T-dualities mapping the system to f-, Q- and R-flux backgrounds.

On Type IIA geometries dual to N = 2 SCFTs

We provide explicit solutions of Type IIA supergravity which are believed to be dual to N=2 superconformal four-dimensional gauge theories. These explicit solutions are based on the general ansatz for such a type of backgrounds introduced by Gaiotto and Maldacena.

= 4 gauged supergravity from duality-twist compactifications of string theory

We investigate the lifting of half-maximal four-dimensional gauged supergravities to compactifications of string theory. It is shown that a class of such supergravities can arise from compactifications of IIA string theory on manifolds of SU(2)-structure which may be thought of as K3 fibrations over T2. Examples of these SU(2)-structure backgrounds, as smooth K3 bundles and as compactifications with H-flux, are given and we also find evidence for a class of non-geometric, Mirror-fold backgrounds. By applying the duality between IIA string theory on K3 and Heterotic string theory on T4 fibrewise, we argue that these SU(2)-structure backgrounds are dual to Heterotic compactifications on a class T4 fibrations over T2. Examples of these fibrations as twisted tori, H-flux and T-fold compactifications are given. We also construct a new set of backgrounds, particular to Heterotic string theory, which includes a previously unknown class of Heterotic T-folds. A sigma model description of these backgrounds, from the Heterotic perspective, is presented in which we generalize the Bosonic doubled formalism to Heterotic string theory.

Conformal field theories in six-dimensional twistor space

Abstract This article gives a study of the higher-dimensional Penrose transform between conformally invariant massless fields on space–time and cohomology classes on twistor space, where twistor space is defined to be the space of projective pure spinors of the conformal group. We focus on the six-dimensional case in which twistor space is the 6-quadric Q in C P 7 with a view to applications to the self-dual ( 0 , 2 ) -theory. We show how spinor-helicity momentum eigenstates have canonically defined distributional representatives on twistor space (a story that we extend to arbitrary dimension). These yield an elementary proof of the surjectivity of the Penrose transform. We give a direct construction of the twistor transform between the two different representations of massless fields on twistor space ( H 2 and H 3 ) in which the H 3 s arise as obstructions to extending the H 2 s off Q into C P 7 . We also develop the theory of Sparling’s ‘ Ξ -transform’, the analogous totally real split signature story based now on real integral geometry where cohomology no longer plays a role. We extend Sparling’s Ξ -transform to all helicities and homogeneities on twistor space and show that it maps kernels and cokernels of conformally invariant powers of the ultrahyperbolic wave operator on twistor space to conformally invariant massless fields on space–time. This is proved by developing the six-dimensional analogue of the half-Fourier transform between functions on twistor space and momentum space. We give a treatment of the elementary conformally invariant Φ 3 amplitude on twistor space and finish with a discussion of conformal field theories in twistor space.

Flux compactifications, twisted tori and doubled geometry

In [1] an O(D,D)-covariant sigma model describing the embedding of a closed world-sheet into the 2D-dimensional twisted torus was proposed. Such sigma models provide a universal description of string theory with target spaces related by the action of T-duality. In this article a six-dimensional toy example is studied in detail. Different polarisations of the six-dimensional target space give different three-dimensional string backgrounds including a nilmanifold with H-flux, a T-fold with R-flux and a new class of T-folds. Global issues and connections with the doubled torus formalism are discussed. Finally, the sigma model introduced in [1], describing the embedding of a world-sheet into , is generalised to one describing a target space which is a bundle of over a base Md, allowing for a more complete description of the associated gauged supergravity from the world-sheet perspective to be given.

Lattice gerbe theory

A bstractWe formulate the theory of a 2-form gauge field on a Euclidean spacetime lattice. In this approach, the fundamental degrees of freedom live on the faces of the lattice, and the action can be constructed from the sum over Wilson surfaces associated with each fundamental cube of the lattice. If we take the gauge group to be U(1), the theory reduces to the well-known abelian gerbe theory in the continuum limit. We also explore a very simple and natural non-abelian generalization with gauge group U(N) × U(N). In the classical continuum limit, it reduces to a free theory, but at non-zero lattice spacing it is an interacting theory which gives rise to U(N) Yang-Mills theory upon dimensional reduction. Formulating the theory on a lattice has several other advantages. In particular, it is possible to compute many observables, such as the expectation value of Wilson surfaces, analytically at strong coupling and numerically for any value of the coupling.

A Superstring Field Theory for Supergravity

A bstractA covariant closed superstring field theory, equivalent to classical tendimensional Type II supergravity, is presented. The defining conformal field theory is the ambitwistor string worldsheet theory of Mason and Skinner. This theory is known to reproduce the scattering amplitudes of Cachazo, He and Yuan in which the scattering equations play an important role and the string field theory naturally incorporates these results. We investigate the operator formalism description of the ambitwsitor string and propose an action for the string field theory of the bosonic and supersymmetric theories. The correct linearised gauge symmetries and spacetime actions are explicitly reproduced and evidence is given that the action is correct to all orders. The focus is on the NeveuSchwarz sector and the explicit description of tree level perturbation theory about flat spacetime. Application of the string field theory to general supergravity backgrounds and the inclusion of the Ramond sector are briefly discussed.

Ambitwistor string theory in the operator formalism

A bstractAfter a brief overview of the operator formalism for conventional string theory, an operator formalism for ambitwistor string theory is presented. It is shown how tree level supergravity scattering amplitudes are recovered in this formalism. More general applications of this formalism to loop amplitudes and the construction of an ambitwistor string field theory are briefly discussed.

On Type IIA geometries dual to N=2N=2 SCFTs

We provide explicit solutions of Type IIA supergravity which are believed to be dual to N=2 superconformal four-dimensional gauge theories. These explicit solutions are based on the general ansatz for such a type of backgrounds introduced by Gaiotto and Maldacena.