CERN-CKC TH Institute on Duality Symmetries in String and M-Theories

3 Aug 2015, 10:00 → 14 Aug 2015, 18:00 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

Hagen Mathias Triendl (CERN), Wolfgang Lerche (CERN)

Over the last few years there has been a growth in developing new geometric concepts associated to ideas coming from string and M-theory. These have included: generalised geometry; double field theory; U-duality manifest formulations of M-theory; extended exceptional geometries; and much more. These developments initially had various motivations including: making duality symmetries manifest in some framework; combining p-form gauge transformations with diffeomorphisms to produce a novel algebraic structure and other ideas concerning making a geometric formulation of gravity and p-form fields together. The key to these developments has been to extend the number of dimensions of spacetime to include novel directions that correspond to winding modes of strings or branes. The developments over the last few years have concentrated on developing the formalism in terms of the production of actions; identifying local symmetries and understanding how to project down from the higher dimensional theory to the usual spacetime description. By now the connection to ordinary supergravity and gauged supergravities in lower dimensions through the embedding formalism is quite well understood.
There are however several key questions that remain and the field is very active. Also, given the extensive development of the formalism, it is now the time to start applying it to problems of interest, in particular to questions concerning compactifications, black holes and fundamental mathematical structures.

 

Organizers: David Berman, Martin Cederwall, Nakwoo Kim, Sang Min Lee, Wolfgang Lerche, Jeong-Hyuck Park, Hagen Triendl

 

Topics:

• the possibility of producing and rigorously investigating genuinely non-geometric backgrounds in double field theory and M-theory equivalents as generalised geometric backgrounds;
• the physical interpretation of DFT in the absence of isometries and localisation in winding space;
• the geometric description of the so called “exotic branes” of deBoer and Shigemori;
• a tool for understanding mirror symmetry;
• the various mathematical structures behind extended and double geometry such as possible non-associative structures;
• new phenomenological implications of non-geometric compactifications;
• the study of cosmological backgrounds
• the understanding of a genuine CFT description of DFT;
• quantum aspects of these theories;
• application of these ideas to black hole physics, thermodynamics and singularity structure;
• what is the global structure of the exceptional geometries both in terms of finite gauge transformations and in terms of a geometric patching to give global solutions.

Monday, 3 August

10:00 coffee break

1 Double Field Theory on Group Manifolds

Speaker: Falk Haßler (MPI for Physics, Munich)

talk.pdf

2 Loops in exceptional field theory

Speaker: Axel Kleinschmidt (MPI Potsdam)

15:00 coffee break

Tuesday, 4 August

10:00 coffee break

3 How many coordinates does DFT have?

I shall describe the puzzles and challenges that rise in attempting to globally patch DFT. Then I shall propose a new class of spaces, the C-spaces, which contain locally the doubled spaces and resolve some of the puzzles. I shall also explain the relation of C-spaces to generalized geometry, and describe how the 3-form flux is geometrised. Some topological aspects of the geometrisation of fluxes, in particular the relation to Whitehead towers, will be explored.

Speaker: Georgios PAPADOPOULOS (Kings College London)

4 T-duality and alpha-prime corrections

I will discuss recent results on T-duality symmetric descriptions of four-derivative terms in string effective actions.

Speaker: Diego Marqués (IAFE Buenos Aires)

Marques-CERN.pdf

15:00 coffee break

17:30 reception

Wednesday, 5 August

10:00 coffee break

5 On (4+6)-dimensional SUSY vacua with non-geometric fluxes

In the 10-dimensional framework of beta-supergravity, we characterize (4+6)-dimensional vacua preserving supersymmetry. We rewrite Killing spinor equations with NSNS non-geometric fluxes using the language of SU(3)*SU(3) structures and Generalized Complex Geometry, in analogy to standard type II supergravities. The NSNS generalized differential operator D that appears exhibits interesting properties, among which being a Generalized Dirac operator. This formulation leads us to a general expression for the superpotential, and we successfully compare it to existing formulas in the literature.

Speaker: David Andriot (MPI, AEI Potsdam-Golm)

Talk CERN.pdf

6 Double field theory and stringy geometry

Speaker: Chris M Hull (Imperial College)

CERN talk.pdf

15:00 coffee break

Thursday, 6 August

10:00 coffee break

7 alpha' corrections in double field theory

Speaker: Olaf Hohm (MIT)

8 Double extension of N=4 super-Yang-Mills theory

Speaker: Soo-Jong Rey (Seoul National University & IBS)

15:00 coffee break

9 Exceptional geometry and Borcherds superalgebras

I will consider generalized diffeomorphisms in exceptional geometry from an algebraic point of view. By extending the U-duality algebra E_n to an infinite-dimensional Lie superalgebra of Borcherds type, the generalized Lie derivatives can be expressed in a simple way, and the expression takes the same form for any n<8. The closure of the transformations then follows from the Jacobi identity and other fundamental properties of this Borcherds superalgebra.

Speaker: Jakob Palmkvist (Texas A&M University)

palmkvist.pdf

Friday, 7 August

10:00 coffee break

10 Consistent Scherk-Schwarz compactifications using exceptional field theory

We discuss 7-dimensional maximal gauged supergravities arising from Scherk-Schwarz compactifications using exceptional field theory. We show how to map consistent compactifications of 10-dimensional type IIA theory into consistent compactifications of 10-dimensional type IIB theory and vice versa and show how this map transforms the resultant gaugings of the 7-dimensional embedding tensor. We use this map to extend the known consistent compactifications of10-dimensional type IIA theory on hyperboloidal spaces $H^{p,q}$ to compactifications of 10-dimensional type IIB theory on such $H^{p,q}$ spaces.

Speaker: Emanuel Malek (LMU Munich)

Talk-v1.pdf

11 E8 geometry

We investigate exceptional generalised diffeomorphisms based on E_8(8) in a geometric setting. The transformations include gauge transformations for the dual gravity field. The surprising key result, which allows for a development of a tensor formalism, is that it is possible to define field-dependent transformations containing connection, which are covariant. We solve for the spin connection and construct a curvature tensor. A geometry for the Ehlers symmetry SL(n + 1) is sketched. Some related issues are discussed. If time allows I will also discuss solution (and relaxation) of the section condition in terms of a twistor transform in a first-quantised setting.

Speaker: Martin Cederwall

15:00 coffee break

Monday, 10 August

10:00 coffee break

12 New gaugings and non-geometry

Speaker: Charles Strickland-Constable (CEA Saclay)

CSC CERN Aug 2015.pdf

13 Conserved charges in double field theory

Speaker: Chris Blair (University of Cambridge)

BlairCERN.pdf

14 Solutions in Extended Field Theories

I will present solutions to Double Field Theory and Exceptional Field Theory and show that the string is a null wave in DFT and the NS5-brane is a monopole. Extending these solutions to EFT where S-duality is part of the symmetry group gives a single self-dual solution combining both the wave and a monopole. Through taking different choices of the section condition, this solution yields all the 1/2 BPS solutions in M-theory.

Speaker: Felix Rudolph (Queen Mary London)

Solutions-FJRudolph.pdf

15 Doubled-yet-gauged and twofold spin groups

Speaker: Jeong-Hyuck Park (Sogang University)

CERN-CKC_2015.pdf

15:00 coffee break

16 Supersymmetric gauged DFT

In a systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the D=10 ungauged maximal and half-maximal supersymmetric double field theories constructed previously. The twisting ansatz may not satisfy the section condition. In addition, the maximal supersymmetric twist requires an extra condition to ensure both the Ramond-Ramond gauge symmetry and the 32 supersymmetries unbroken. Based on http://arxiv.org/abs/1505.01301

Speaker: Jose J. FERNANDEZ-MELGAREJO (Harvard University)

presentation.pdf

Discussion Session

Tuesday, 11 August

10:00 coffee break

17 Weakly Constrained Double Field Theory

Speaker: Kanghoon Lee (Korea Institute for Advanced Study)

weakDFT-CERN.pdf

18 TBA

Speaker: Edvard Musaev (Higher School of Economics, Faculty of Mathematics, Moscow)

19 Double Sigma Model

Double sigma model with strong constraints is equivalent to the ordinary sigma model by imposing a self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We combine the antisymmetric background field with the field strength to redefine the generalized metric. We use this generalized metric to construct a consistent double sigma model with boundary conditions. We also give comments to non-commutative geometry in the double sigma model.

Speaker: Chen-Te Ma (National Taiwan University)

double sigma model.pdf

15:00 coffee break

20 Holographic Entanglement entropy and central charge in CFT's

Speaker: Mohsen Alishahiha (IPM Teheran)

Alishahiha.pdf

Discussion Session

Wednesday, 12 August

10:00 coffee break

21 Gauging of 2D sigma models without isometry and genuinely non-geometric backgrounds from 3D sigma models.

In this talk we discuss two problems in the context of sigma models motivated by recent studies in T-duality and non-geometry. The first problem refers to the gauging of 2D sigma models when there is no isometry available, while the second regards the possibility to construct genuinely non-geometric backgrounds with the aid of 3D sigma models. In both cases the underlying mathematical framework is the theory of Lie and Courant algebroids, which will be presented in the first part of the talk. Then we shift our attention to a general class of 2D theories called Dirac sigma models and present a novel way to gauge such theories. This gauging is useful in formulating T-duality even when there is no isometry. Finally we discuss the correspondence between Courant algebroids and AKSZ membrane models with boundary. A certain class of such theories offers the possibility to construct non-geometric models which do not possess a geometric dual.

Speaker: Athanasios CHATZISTAVRAKIDIS (Leibnitz University Hannover)

22 Metastring theory

Speaker: Rob Leigh (University of Illinois)

CERN_2015.pdf

15:00 coffee break

Thursday, 13 August

10:00 coffee break

23 Enhanced gauge symmetry and winding states in Double Field Theory

Speaker: Jose Alejandro ROSABAL RODRIGUEZ (Universidad de Buenos Aires)

talk_CERN_Rosabal.pdf

24 U-gravity for SL(N)

We construct a duality manifest gravitational theory for the special linear group, SL(N) with N≠4. The spacetime is formally extended, to have the dimension 12N(N−1), yet is `gauged'. Consequently the theory is subject to a section condition. We introduce a semi-covariant derivative and a semi-covariant `Riemann' curvature, both of which can be completely covariantized after symmetrizing or contracting the SL(N) vector indices properly. Fully covariant scalar and `Ricci' curvatures then constitute the action and the `Einstein' equation of motion. For N≥5, the section condition admits duality inequivalent two solutions, one (N−1)-dimensional and the other three-dimensional. In each case, the theory can describe not only Riemannian but also non-Riemannian backgrounds.

Speaker: Yoonji Suh (Sogang University)

slN_CERN.pdf

15:00 coffee break

Friday, 14 August

10:00 coffee break

25 Codimension two solutions in five-dimensional supergravity

We study a new class of supersymmetric solutions in five-dimensional supergravity representing multi-center configurations of codimension-2 branes along arbitrary curves. Codimension-2 branes are produced in generic situations out of ordinary branes of higher codimension by the supertube effect and, when they are exotic branes, spacetime generally becomes non-geometric. The solutions are characterized by a set of harmonic functions on R^3 with non-trivial monodromies around codimension-2 branch-point singularities. The solutions can be regarded as generalizations of the Bates-Denef/Bena-Warner multi-center solutions with codimension-3 centers to include codimension-2 ones. We present some explicit examples of solutions with codimension-2 centers, and discuss their relevance for the black microstate (non-)geometry program. ref: 1505.05169

Speaker: Masaki Shigemori (Kyoto University)

20150814 CERN 'Codimension-2 solutions in five-dimensional supergravity'.pdf

15:00 coffee break