ESI Higher Structures in String Theory and Quantum Field Theory

Main Workshop Dec. 7 - Dec. 11, 2015


David Berman (QMUL) Chris Rogers (Louisiana)
Andreas Deser (Hannover) Jonathan Rosenberg (Maryland)
Keith Hannabuss (Oxford) Urs Schreiber (Prague)
Dieter Luest (LMU) Christoph Schweigert (Hamburg)
Jouko Mickelsson (Helsinki) Guo Chuan Thiang (Adelaide)
Erik Plauschinn (LMU) Konrad Waldorf (Greifswald)
Peter Prešnajder (Comenius University) Maxime Zabzine (Uppsala)
Patricia Ritter (Bologna)

Erwin Schroedinger Lecture: On Thursday December 10, Daniel Huybrechts (Bonn) will give a lecture `Symmetries and K3 Surfaces' from 5:00 - 6:15 pm in the Boltzmann Lecture Theatre at the ESI. See this link for more details. The lecture will be followed by a festive reception.


All talks will be in the Boltzmann Lecture Theatre at the ESI

Dec. 7 - 11

10:00 - 11:00 am
Morning Tea 11:00 - 11:30 am
11:30 am - 12:30 pm
Lunch 12:30 - 2:00 pm
2:00 - 3:00 pm
Afternoon Tea 3:00 - 3:30 pm
3:30 - 4:30 pm

5:00 - 6:15 pm

*Erwin Schroedinger Lecture

Important Note: Tuesday December 8 is a public holiday in Vienna, therefore ESI will be closed on this day.

Workshop Dinner: On the evening of Tuesday December 8 there will be a dinner at a local heuriger. Details will follow in due course.

Titles and Abstracts

Berman : `Aspects of Double and Exceptional Field Theory'

Abstract: We review the double and exceptional field theory framework with an emphasis on open problems and the relation to higher structures.

Deser: `Star products on graded manifolds and deformations to Courant algebroids from string theory'

Abstract: Deformations of Courant algebroids are of interest in both, string theory and mathematics. It was realized by Roytenberg, that Lie bialgebroids and their associated Courant algebroids can be characterized by a homological vector field on the cotangent bundle of the parity reversed version of the underlying Lie algebroid. This lead to the introduction of the Drinfel'd double of a Lie bialgebroid. In a similar way, we show that the C-bracket of double field theory can be represented by a derived bracket construction using the canonical Poisson structure on the Drinfel'd double of the underlying Lie-bialgebroid. As a consequence of this result, we are able to apply a graded version of the Moyal-Weyl star product to compute a first order deformation of the C-bracket. Remarkably, this coincides with the first order correction in the string coupling parameter found recently in string theory.

Hannabuss: `T-duality: geometry, C*-algebras, and tensor categories'

Abstract: Our mathematical understanding of T-duality has progressed in stages, as different features have been explored. This talk will follow one of the paths taken, which starts within geometry, then connects with known features of C*-algebra theory, and finally seems to lead into tensor categories. Each of these jumps is motivated by the need to eliminate a previous constraint. The final part of the talk will be more speculative.

Luest: `Some world sheet aspects of double field theory and closed string non-commutativity',

Abstract: In this talk we discuss a possible world sheet description of double field theory in terms of gauged non-linear sigma-models. We also discuss how closed string non-commutativity/non-associativity emerges in the context of the sigma-model description of non-geometric string backgrounds.

Mickelsson: `Locally smooth group cohomology, gerbes and central extensions'

Abstract: A central extension of a Lie group (a loop group, for example) can be described using a locally smooth group cocycle of degree 2. In the same way, gerbes over Lie groups lead to locally smooth 3-cocycles. Furthermore, the gerbal group cocycle can be derived from a locally smooth 2-cocycle of an infinite dimensional Lie group. Examples for the case of groups of gauge transformations are discussed.

Plauschinn: `Collective T-duality transformations'

Abstract: We study collective T-duality transformations from a string world-sheet perspective, by following Buscher's procedure of gauging a symmetry and integrating-out the gauge field. We find various constraints, and discuss them for the example of the three-torus and the three-sphere. We pay special attention to the question whether and how non-geometric backgrounds arise.

Erik Plauschinn has kindly made available the slides from his talk here

Prešnajder: `From Noncommutative Quantum Mechanics towards Noncommutative QFT'

Abstract: Various physical theories can be considered as deformations of classical Newton mechanics (CM) with deformations parameters being the fundamental constants ℏ, c-1 and λ. For example, QFT can be considered as the deformation of CM with non-vanishing ℏ and c-1. NC QFT is usually assumed as a deformation of QFT by λ ≠ 0 which is not yet fully described. I shall describe NC QM a well defined λ-deformation of QM that has been formulated recently, and I shall discuss an alternative way to NC QFT, the c-1-deformation of NC QM.

Ritter: `Strong homotopy algebras of local observables (shlalos) and Vinogradov algebroids'

Abstract: We are interested in the categorification of the Poisson algebra of local observables on symplectic manifolds, in view of a better understanding of the quantization problem on multi-symplectic manifolds. We will therefore review truncated strong homotopy Lie algebras (or Lie n-algebras) and their homomorphisms, focusing in particular on the shlalo associated to n-plectic manifolds. This will allow us to relate higher shlalos to the Lie n-algebras associable to twisted Vinogradov algebroids, generalising the embedding of the Lie 2-algebra of observables on 2-plectic manifolds into the 2-algebra of global sections of twisted Courant algebroids.

Rogers: `Equivariant cohomology and homotopy moment maps'

Abstract: Atiyah and Bott famously observed that cocycles representing degree 2 classes in equivariant de Rham cohomology correspond to moment maps in (pre-)symplectic geometry. From the point of view of geometric quantization, moment maps provide a way to lift infinitesimal symmetries of a classical system to a corresponding quantum one. In this talk, I will describe a generalization of the Atiyah-Bott correspondence that uses the homotopy theory of L infinity algebras to produce so-called "homotopy moment maps" from higher degree equivariant classes. If time permits, I will then discuss the relationships between homotopy moment maps and equivariant bundle n-gerbes (and their role in gauging sigma models). This is based on joint work with M. Callies (Goettingen), and separate joint work with K. Waldorf (Greifswald).

Rosenberg: `Duality of twisted orientifolds'

Abstract: Orientifold string theories are string theories on a spacetime target space equipped with an involution. Usually (up to an uninteresting flat factor) this spacetime is taken to be a Calabi-Yau manifold with a holomorphic or anti-holomorphic involution. D-brane charges in such theories live in Atiyah's KR-theory and its twisted variants. We discuss the form of these topological twists and T-duality of these theories in the simplest case where the Calabi-Yau manifold is an elliptic curve. We also discuss a kind of algebraic mirror symmetry analogue. Some of this is joint work with Chuck Doran and Stephan Mendez-Diez.

Schreiber: `Generalized cohomology of M2/M5-branes'

Abstract: While it has become well-known that the charges of F1/Dp-branes in type II string theory need to be refined from de Rham cohomology to certain twisted generalized differential cohomology theories, it is an open problem to determine the generalized cohomology theory for M2/M5-branes in 11 dimensions. I discuss how a careful re-analysis of the old brane scan (arXiv:1308.5264 , arXiv:1506.07557, joint with Fiorenza and Sati) shows that rationally and unstably, the M2/M5 brane charge is in degree-4 cohomotopy. While this does not integrate to the generalized cohomology theory called stable cohomotopy, it does integrate to G-equivariant stable cohomotopy, for G a non-cyclic finite group of ADE type. Generally, such an equivariant cohomology theory needs to be evaluated on manifolds with local ADE orbifold singularities, and picks up contributions from the orbifold fixed points. Both of these statements are key in the hypothesized but open problem of gauge enhancement in M/F-theory.

Schweigert: `State sum constructions of extended topological field theories and defects'

Abstract: Surface defects in (extended) three-dimensional topological field theories have important applications, ranging from solid state physics to representation categories. The intersection of such defects is the location of a generalized Wilson line. Categories in which labels for these Wilson lines are constructed, for topological field theories of Turaev-Viro type, by a 2-functor that assigns to a bimodule category over a finite tensor category a k-linear category, which can be seen as a catetgorified trace. This 2-functor also enters crucially into the construction of conformal blocks.

Thiang: `T-duality, K-theory, and bulk-boundary correspondence for topological phases'

Abstract: K-theory groups of various flavours appear in the study of topological phases in condensed matter physics. This is analogous to the situation for D-brane charges in string theory, and suggests that the idea of T-duality can be utilised in the condensed matter context. One example is the notion of dual topological phases, which may be accompanied by a "symmetry change". A second example is the simplification of the bulk-boundary map into a restriction map under a T-duality transformation, in several cases of physical interest.

Waldorf: `String structures and supersymmetric sigma models'

Abstract: Supersymmetric sigma models suffer from a "global fermionic anomaly" meaning that its Feynman amplitude is not a function but a section in a line bundle. In 1987 Killingback proposed a cancellation mechanism using a "string structure" on the target space. I will explain why and how we nowadays understand a string structure as a higher-categorical structure.

Zabzine: `Integrals, matrix models and deformed Virasoro algebra'

Abstract: I will present the simple toy model which explains the relation between one-dimensional integrals and the Virasoro algebra. Then I will review the appearance of the Virasoro constraints in Hermitian matrix model. I will discuss the deformations of Virasoro algebra and its appearance in different matrix models/integrals. If time allows I will discuss different super-generalisations of this construction.