Algebraic structures in higher-spin gravity

UNUSUAL LOCATION (due to clash with MSc presentations): JCMB 1501

Higher-spin gravity refers to an extension of general relativity involving fields with spin higher than two. The problem of finding a consistent interacting theory of higher-spin gravity can be reformulated into algebraic terms, whose solution is surprisingly simple and rigid. We first describe the construction of a higher-spin symmetry algebra in the case of exact higher-spin symmetry, and make some comments regarding its holographic interpretation. We then turn to the problem of ``slightly broken'' higher-spin symmetry, which involves a certain deformation of the infinite-dimensional symmetry into a $A_\infty$ algebra.