Talks and Schedule
09.20 - 09.30 - Opening
Morning Session, Chair: Nihat Sadık Değer, Boğaziçi University, Mathematics Department
09.30 - 10.20 - Per Sundell - Holographically Entangled Vacuum States in Higher-spin Gravity
Biobio University, Department of Physical Sciences
Abstract: We propose to second-quantize Vasiliev's higher-spin gravity, which is a classical gauge theory with moduli spaces consisting of noncommutative, first-quantized geometries, using a natural generalization the Alexandrov--Kontsevich--Schwarz--Zaboronski solution to the Batalin--Vilkovisky master equation in the form of ambi-dimensional partition functions including efects. These functions provide functors from Cartan integration modules in the form of Lie groupoids to direct products of (second-quantized) operator algebras attached to (first-quantized) defects. The functors intertwine the actions of globally defined operators on different defects resulting in overlap conditions whose solutions are entangled vacuum states. As an application, we consider a five-dimensional fractional-spin gravity model that contains co-dimension one defects with higher-spin gravity fields and co-dimension two defects with conformal matter fields coupled to topological conformal higher spin fields and colour fields, entangled by means of overlap conditions induced by Chern classes for super-connections. The resulting vacuum state provides a direct realization of the holographic correspondence between the four- and three-dimensional quantum field theories reducing in the leading order to the proposed correspondence between Vasiliev's theory and free fields; the structure of the first sub-leading order corroborates the proposal of Klebanov--Polyakov.
10.30 - 11.20 - Amihay Hanany - Magnetic Quivers and Higgs Branches at Infinite Coupling
Imperial College London, Physics Department
Abstract: We will look at simple supersymmetric gauge theories in 5d and 6d with 8 supercharges and see how their Higgs branch critically changes when the gauge coupling is tuned to be infinite (alternatively, the inverse coupling is tuned to be 0). In 5d massless instantons modifies the Higgs branch by changing the number of massless states. In 6d tensionless strings lead to Higgs branches with two critical phenomena: 1 — The small instanton transition. 2 — Discrete Gauging.
11.30 - 12.20 - Edvard Musaev - Boundary Conditions in AdS/CFT Correspondence
Moscow Institute of Physics and Technology, Laboratory of High Energy Physics
Abstract: Behavior of a scalar field on a fixed AdS space-time background is regulated by two modes, usually referred to as normalizable and non-normalizable. In the standard AdS/CFT prescription the normalizable mode corresponds to a one-point correlation function on the CFT side, while the non-normalizable becomes the boundary data. In this fashion only operators of the conformal weight \Delta_+ can be described. In the work hep-th/9905104 a relation between the prescription and the choice of boundary conditions has been demonstrated and it has been shown that for Neumann boundary conditions the prescription reverses and allows to describe operators of weight \Delta_-. In this talk I will review the formalism and demonstrate the relation between the choice of boundary conditions and the prescription for correlators explicitly using the renormalization procedure of Skenderis and Papadimitriou. A short review of generalization of the picture to asymptotically locally AdS space-times will be provided.
12.30 - 14.00 - Lunch Break
Afternoon Session, Chair: Aybike Çatal-Özer, Istanbul Technical University, Mathematics Department
14.00 - 14.50 - Keremcan Doğan - A Dual Calculus Perspective on Algebroids
Istanbul Technical University, Mathematics Department
Abstract: In this talk, we extend the notion of Lie bialgebroids for arbitrary vector bundles. We achieve this by formalizing the notion of dual calculus on algebroids of split form. We write down explicit compatibility conditions, and construct an algebroid, which we dub as “exceptional Drinfel’d algebroid”, after a detailed analysis of most general forms of algebroid axioms. These can be considered as the generalizations of the special case of triangular Lie bialgebroids, and we relate them to the notion of exceptional Drinfel’d algebra, with a particular focus on the simplest -SL(5)- case. After briefly mentioning a possible extension for the global picture in the framework of rackoids, we conclude the talk with some possible future works.
15.00 - 15.50 - Cem Yetişmişoğlu - Supergeometry and Discrete Dynamical Systems
Istanbul Technical University, Mathematics Department
Abstract: In this talk, we will introduce abstract notions of laboratories, states and measurements. We then describe these notions on symplectic manifolds which is a natural ground for studying mechanical systems. Moreover we will introduce odd dimensional counterparts of symplectic manifolds which allow for covariant treatment of dynamical systems. Finally, we will talk about supermanifold geometry and how these constructions can be generalized to cover treatment of dynamical discrete systems.
16.00 - 16.50 - Kadri İlker Berktav - Shifted Contact Structures
Istanbul Technical University, Mathematics Department
Abstract: In this talk, we outline a general framework for derived algebraic geometry and explain how to define familiar geometric structures in this context. As an important case, we discuss derived symplectic geometry and present some key results. With the same spirit, we also mention some of our work in this research direction.