Dra. Rodríguez-Durán, Evelyn

A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincaré algebra is presented. The -extended Poincaré supergravity is obtained by expanding the super Lorentz theory. We extend our procedure to their respective asymptotic symmetries and show that the super-BMS3 appear as expansions of one Virasoro superalgebra. Interestingly, the -extended super-BMS3 obtained here are not only centrally extended but also endowed with internal symmetry. We also show that the -extended super Poincaré algebras with both central and automorphism generators are finite subalgebras.

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač–Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.