Regular Seminar Elizabeth Himwich (Harvard)
at: 13:45 room Online abstract: | The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w(1+infinity). In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of w(1+infinity) on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons. |
Regular Seminar Vladimir Dobrev (Bulgarian Academy of Sciences)
at: 12:00 room Zoom abstract: | The main purpose of the present talk is to lay the foundations of generalizing the AdS/CFT (holography) idea beyond the conformal setting, where it is very natural. The main tool is to find suitable realizations of the bulk and boundary via group theory. We use all ten families of classical real semisimple Lie groups G and Lie algebras g. For this are used several group and algebra decompositions: the global Iwasawa decomposition and the local Bruhat and Sekiguchi decomposititions, which we introduce first on easy examples. The same analysis is applied to the exceptional real semisimple Lie algebras. We present the boundary-to-bulk operators first in the Euclidean conformal setting and then outline the various generalizations. |