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SCGP Weekly Talk: Leonardo Rastelli, YITP

Title: The superconformal bootstrap and vertex operator algebras
Speaker: Leonardo Rastelli, YITP
Date: Tuesday, October 14, 2014
Time: 01:00pm Р02:00pm
Place: Lecture Hall 102, Simons Center


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Abstract: Conformal field theories (CFTs) play a central role in theoretical physics. They are the signposts in the larger space of quantum field theories, which can be understood as renormalization group trajectories between two conformal points. A CFT is characterized by the associative algebra of its local operators, a structure that we can hope to define to the satisfaction of a mathematician. Indeed this notion has already been made completely rigorous for (the chiral half of) a two-dimensional CFT, leading to the definition of vertex operator algebras.

After a general introduction, I will outline the emerging bootstrap program for four- and six-dimensional CFTs with extended supersymmetry. Remarkably, these higher-dimensional quantum field theories admit closed operator subalgebras isomorphic to two-dimensional vertex operator algebras. This observation brings established algebraic tools to bear on difficult physical questions. Conversely, physical dualities imply a new rich set of conjectures about vertex operator algebras.