Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Preprint 2013-25



Infinite chiral symmetry in four dimensions.


Chris Beem, Madalena Lemos, Pedro Liendo, Wolfger Peelaers, Leonardo Rastelli, Balt van Rees.


Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2013-25


MSC 2000:


Abstract: We describe a map from the space of four-dimensional superconformal field theories with extended supersymmetry to the space of two-dimensional chiral algebras. Correlators of the chiral algebra compute correlators in a protected sector of the parent four-dimensional theory. The operators captured by the chiral algebra are precisely the operators that contribute to the Schur limit of the superconformal index, and the crossing symmetry constraints of the chiral algebra impose very stringent requirements on their spectrum and OPE coefficients. This connection leads to novel unitarity bounds for the central charges of four-dimensional interacting superconformal field theories. The four-point functions of the chiral algebra are precisely the ingredients needed as inputs to the numerical bootstrap program for unprotected operators. We characterize the chiral algebras associated to Lagrangian theories via a cohomological construction, and also sketch the structure of the chiral algebras associated to the superconformal field theories of class S. For several examples we conjecture descriptions of the chiral algebras as W-algebras.


Keywords: conformal field theory, supersymmetry, chiral algebra, vertex operator algebra, conformal bootstrap