W symmetry in six dimensions

© 2015, The Author(s). Abstract: Six-dimensional conformal field theories with (2, 0) supersymmetry are shown to possess a protected sector of operators and observables that are isomorphic to a two-dimensional chiral algebra. We argue that the chiral algebra associated to a (2, 0) theory labelled by the simply-laced Lie algebra g$$ \mathfrak{g} $$ is precisely the W$$ \mathcal{W} $$ algebra of type g$$ \mathfrak{g} $$, for a specific value of the central charge. Simple examples of observables that are made accessible by this correspondence are the three-point functions of half-BPS operators. For the A<inf>n</inf> series, we compare our results at large n to those obtained using the holographic dual description and find perfect agreement. We further find protected chiral algebras that appear on the worldvolumes of codimension two defects in (2, 0) SCFTs. This construction has likely implications for understanding the microscopic origin of the AGT correspondence.