Schedule for: 17w5018 - String and M-theory geometries: Double Field Theory, Exceptional Field Theory and their Applications

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

I show that in bosonic string theory there is a conflict at first order in alpha' between manifest background independence and manifest T-duality invariance in terms of the standard massless fields, metric, b-field and dilaton. A double field theory formulation of the bosonic string nevertheless exists in terms of an \alpha'-deformed frame or vielbein formalism.

I will review higher-derivative extensions of Double Field Theories that encompass the first order corrections to the heterotic and bosonic strings in a unified framework. I will then explore applications of the formalism, with emphasis on how to compute higher-derivative corrections to gauged supergravities through generalized Scherk-Schwarz compactifications.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

World-sheet superstring and target-spacetime supergravities have been fully reformulated and generalized in doubled-yet-gauged coordinates. DFT appears as a string theory extension of, and possibly an alternative to, Einstein gravity. I will review my related recent works (1606.09307, 1609.04265), which in particular includes a `uroboros' solution to the dark matter problem.

Recently proposed exceptional field theories (EFTs) making manifest the duality $E_{n(n)}$ symmetry, first observed as nonlinearly realized symmetries of the maximal $d=3,4,...,9$ supergravity ($n=11-d$) and containing 11D and type IIB supergravity as sectors, were formulated in enlarged spacetimes. In the case of $E_{7(7)}$ EFT such an enlarged spacetime can be identified with the bosonic body of the $d=4$ central charge superspace $\Sigma^{(60|32)}$, the ${\cal N}=8$ $d=4$ superspace completed by 56 additional bosonic coordinates associated to central charges of the maximal $d=4$ supersymmetry algebra. In this talk we show how the hypothesis on the relation of all the known $E_{n(n)}$ EFTs, inclusing $n=8$, with supersymmetry leads to the conjecture on existence of 11D exceptional field theory living in 11D tensorial central charge superspace $\Sigma^{(528|32)}$ and underlying all the $E_{n(n)}$ EFTs with $n=2,...,8$, and probably the double field theory (DFT). We conjecture the possible form of the section conditions of such an 11D EFT and show that quite generic solutions of these can be generated by superparticle models the ground states of which preserve from one half to all but one supersymmetry. The properties of these superparticle models are briefly discussed. We argue that, upon quantization, their quantum states should describe free massless non-conformal higher spin fields in D=11.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

DFT/EFT are known to be reduced to the standard descriptions by introducing appropriately parameterized generalized metric and by applying suitably chosen section conditions. We generalize this development to non-geometric backgrounds by utilizing dual fields pertinent to non-geometric fluxes. We introduce different parameterizations for the generalized metric, in terms of the conventional supergravity fields or the dual fields. Under certain simplifying assumptions, we construct new effective action for non-geometric backgrounds. We then obtain the non-geometric backgrounds sourced by exotic branes. From them, we construct their U-duality monodromy matrices. The charge of exotic branes obtained from these monodromy matrices agrees perfectly with the charge obtained from the non-geometric flux integral.

We discuss the explicit map between marginal deformations of generic N=1, d=4 SCFTs and structures in exceptional generalised geometry that describe supersymmetric AdS backgrounds in both 11-dimensinal and type IIB supergravity.

It is well known that, in the absence of internal fluxes, supersymmetric Minkowski backgrounds are given by manifolds with special Riemannian holonomy, such as the celebrated Calabi-Yau spaces. I will present recent work showing that general supersymmetric Minkowski flux backgrounds are precisely the analogues of these in generalised geometry. The generalised holonomy group is simply the natural stabiliser group of the Killing spinors, and depends only on the dimension and the number of preserved supersymmetries. The Killing superalgebra, which has a neat manifestation in this language, plays a key role in the proof of the main result for N > 2 supersymmetry and we are able to fix its form explicitly using this technology.

Recent advances have made it possible to finally understand the physicists' concept of generalized Kahler potential in precise mathematical terms. I will describe how this can be done once we understand the notion of symplectic Morita equivalence between Poisson manifolds. Another benefit of the study is a new formalism for thinking of generalized Kahler geometry as a whole.

Based on a diferent vacuum choice we construct, using the old and the new covariant quantization, the world sheet version of the HZS double field theory. We compute the scatering amplitude of n-massless scalars and the one loop partition function. A new interpretation is given to this string theory. We also point out the relation with the ambitwistor string as the tensionless limit version of this string theory.

Why Double Field Theory might be useful in Early Universe Cosmology....

One of the most powerful applications of exceptional and double field theories has been in the study of consistent truncations via generalised Scherk-Schwarz reductions which preserve all supersymmetries. In this talk I will show how to generalise the Scherk-Schwarz procedure to define consistent truncations which break half the supersymmetries. This allows for the study of exceptional field theories on CY-surfaces and their torsion-full counterparts. Finally, I will discuss how one can use the truncation procedure to reduce exceptional field theory to heterotic double field theory, corresponding to the heterotic / M-theory duality.

A key feature of string theory which can be understood naturally in DFT is the presence of exotic branes (or T-folds), for instance the 5_2^2 which is obtained by two T-dualities from the NS5 brane. The electric dual of this exotic brane can be identified with a ``negative string'' solution obtained by dualising the worldvolume directions -- including time -- of the fundamental string supergravity solution. It has been recently argued by Dijkgraaf et al that such negative branes can be understood as being surrounded by a ``bubble'' in which physics is described by various exotic string theories originally considered by Hull. Focusing on the negative string solution, I will discuss the DFT description of such exotic objects, including writing down a novel variant of DFT which applies in theories where fundamental strings are Euclidean.

Exceptional field theories are manifestly duality covariant formulations of supergravity that have proven powerful in addressing various problems in supergravity theories. Among their applications I discuss consistent truncations of (super)gravity, higher dimensional origins of dyonic gauged supergravities, and generalised type II supergravity.

A doubled space which in addition to a neutral metric \eta and a generalized metric H contains a symplectic structure \omega has been dubbed a Born geometry. We construct the unique and fully determined connection compatible with these three objects and vanishing generalized torsion. The latter is related to an integrability condition on the structures of the doubled space. Double Field Theory can be seen as a limit of Born geometry where the symplectic form is constant. Hence the Born connection provides a unique connection for DFT.

I will set out a list of open problems in the area and the various different approaches people have taken. The session will then be open for participants to contribute further problems, ideas, research directions and solutions.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.