Speakers and Abstracts

Day 1: Classical and Quantum Integrability

Sibylle Driezen (IGFAE, Univ. de Santiago de Compostela)

An introduction to Classical Integrability (in Sigma Models)

In this lecture I will introduce the salient features of 2d classical integrable field theories. These models are distinguished by the rare property of having an infinite tower of conserved charges that are in involution and, therefore, in a certain sense completely solvable. In particular, I will cover the notions of Lax connections, monodromy matrices and Maillet brackets. I will illustrate these concepts with the Principal Chiral Model which is a two-dimensional integrable sigma model relevant for string theory and the AdS/CFT correspondence. At the end I will give a broad overview of deformations of sigma models of which the integrable structure is preserved.

Stijn Van Tongeren (Humboldt University)

Exact S matrices and spectra of integrable models

Despite their special properties, integrable field theories are hard to quantize explicitly. Instead such theories are typically tackled by the integrable S-matrix bootstrap. I will give an overview of this approach, and discuss how it allows us to find the spectum of an integrable quantum field theory. This will take us from factorized scattering, to various forms of the Bethe ansatz. Time permitting, I will finish with a sketch of how these methods were applied to get one of the great successes of AdS/CFT: determining the spectrum of scaling dimensions of 4D N=4 super Yang-Mills theory nonperturbatively.

Sylvain Lacroix (Hamburg University)

Affine Gaudin models

In this talk, I will give an introduction to the formalism of affine Gaudin models and its application to the study of integrable sigma models. I will start by reviewing the concept of Maillet bracket with twist function, which describes the Hamiltonian structure of integrable sigma models. I will then explain how this naturally leads to affine Gaudin models and discuss their construction. Finally, I will describe on a concrete example how integrable sigma models can be seen as realisations of such affine Gaudin models and discuss how this formalism can be used to construct new integrable sigma models.

Day 2: Double and Exceptional Field Theory

Chris Blair (Vrije Univ. Brussel)

Introduction to T/U-duality invariant formalisms

I will give an introduction to double and exceptional field theory, and explain to what extent the title of this talk is accurate. Based on the review 2006.09777.

David Osten (ITMP, Lomonosov Moscow State Univ.)

Introduction to non-geometric backgrounds in string theory

More general backgrounds than those of Riemannian geometry are well-defined in string theory, as also string dualities may be allowed for glueing coordinate patches. For that reason such backgrounds are typically called T- resp. U-folds. They can be described in terms of so-called generalised fluxes, a generalisation of the standard description of geometric backgrounds via metric and H-flux in bosonic string theory.

The first part of the talk introduces T- and U-folds and their characterisation by non-geometric (generalised) fluxes in simple toy models. Several non-trivial examples of T-folds in string theory are discussed, including integrable sigma models as non-geometric flux backgrounds and the role of the generalised fluxes in (flux) compactifications.The second part of this review talk is concerned with non-commutative and non-associative structures and how these can be realised in the phase space of a string in non-geometric backgrounds.

Justin Kaidi (Stony Brook Univ.)

Introduction to Exotic Branes

In addition to the familiar D-branes, U-duality demands the existence of a full panoply of non-perturbative objects known as ``exotic” branes. Despite their name, these exotic branes are ubiquitous in string theory, appearing in even mundane processes such as the brane polarization effect. Exotic branes also feature prominently in the counting of blackhole microstates, à la the fuzzball program. In this talk we introduce the basic features of exotic branes, and discuss their connection to non-geometric backgrounds of string theory.

Day 3: Generalised Geometry and Homotopy Algebras

David Tennyson (Imperial College London)

An Introduction to Generalised Geometry and G-structures

Generalised geometry is the natural framework in which to study backgrounds of string theory. It naturally encompasses the exceptional symmetries that arise, as well as the extended gauge structure generated by the higher form gauge fields. All objects in generalised geometry can be viewed as sections of vector bundles transforming in some representation of the symmetry group. The representations of physical significance appear in the tensor hierarchy of exceptional field theory. Of particular importance is the generalised tangent bundle E --> M, which is an extension of the tangent bundle by differential forms, sections of which generate gauge transformations through the Dorfman derivative. In this overview talk, I will carefully introduce these objects, as well as other bundles that will be of importance later in the discussion. After this, I will move on to a principle that is central to many discussions in generalised geometry - the idea of a G-structure. A G-structure can be viewed as a refinement of the geometry and, after providing a definition, I will briefly demonstrate why they are so important in the discussion of string backgrounds with a few examples. Throughout the talk I will try to provide as much intuition as I can, providing parallels with conventional geometry to demystify some of the complicated looking constructions.

Alex S. Arvanitakis (Vrije Univ. Brussel)

Homotopy algebras in geometry and physics

I will provide a brief introduction to homotopy algebras and point out a few of their natural appearances in quantum field theory, (generalised) geometry, and string theory. Two major take-aways will be: how the algebraic structure of gauge symmetry in diverse contexts is governed by homotopy algebras, and how non-isomorphic --- but equivalent --- homotopy algebras can describe mutually dual physical theories.

Future Career Oriented Speakers

PhD Gong Shows (chronologically)