A New Class of QFTs: Cluster Algebras, the Grassmannian and Beyond

Sebastian Franco (Durham University)

Tuesday 6th May, 2014 15:00-16:00 Maths 326

Abstract

Over the last decade, we have witnessed remarkable progress in our understanding of Quantum Field Theories. New insights have emerged from a multitude of fronts, ranging from the Gauge/Gravity Correspondence to Integrability.  In this seminar I will discuss Bipartite Field Theories (BFTs), a new class of QFTs embodying many of these new approaches. BFTs are 4d, N=1 quiver gauge theories with Lagrangians defined by bipartite graphs on Riemann surfaces. Remarkably, they underlie a wide spectrum of interesting topics, including: D-branes probing Calabi-Yau manifolds, their mirror configurations, integrable systems in (0+1) dimensions and the Grassmannian formulation of scattering amplitudes in N=4 SYM. I will introduce new techniques for studying these gauge theories. I will explain how their dynamics is captured graphically and the interesting emergence of concepts such as Calabi-Yau manifolds, the Grassmannian and cluster algebras.

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