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Geometry of (S)QFT: September 20-24, 2021

Organized by: Ibou Bah and Shlomo Razamat

Quantum field theory (QFT) is a universal language used to describe a wide variety of phenomena in Nature, including elementary particles, condensed matter systems, and cosmology. Despite its remarkable successes, novel toolkits are needed for exploring the landscape of QFTs and for computing and characterizing generic observables, particularly when they are strongly coupled. This is highlighted by recently developed exact techniques for supersymmetric QFTs (SQFTs) and string theory, which have shown that conventional methods based on Lagrangians and perturbation theory fail to capture the rich structure of the QFT framework. This is true especially when one insists on symmetries of the system to be manifest. A dramatic example is the rich zoo of interacting QFTs in d > 4 spacetime dimensions which cannot be constructed using conventional methods. However, they are firmly established thanks to a variety of complementary approaches, including top-down constructions in string theory and holography, as well as bottom-up QFT arguments. Compactifications of these theories lead to even richer classes of strongly coupled theories in d ≤ 4, make manifest vast and extensive networks of dualities and RG flows, and bring to fore fundamental interconnected-ness that underlies the space of QFTs. The common thread in this progress is the interplay between geometry and physics, particularly in the construction and study of SQFTs. We propose to organize a workshop at the Simons Center for Geometry and Physics on the theme of geometry of (S)QFT. In this workshop we intend to discuss these exciting advances. In particular we will discuss aspects of geometric nature of extra dimensions of string theory, holographic constructions of SCFTs, geometrical constructions of SCFTs in lower dimensions, and the geometry of moduli spaces and space of couplings.