Speaker: Pedro Álvarez. Universidad San Sebastián, Valdivia, Chile.
This talk offers a pedagogical introduction to geometric realizations of supersymmetry in the adjoint representation. We begin with the basic framework and explain how gravity, Yang–Mills fields, and fermionic matter can be combined in an osp(N|4)-valued superconnection. We then introduce the Clifford construction of the action, emphasizing how it relates the gravity, gauge, and matter sectors.
Next, we explain the role of the Clifford-valued coframe e^a\gamma_a in relating vector and spinor representations of local Lorentz symmetry. We show how its exterior products generate the building blocks of chiral gravity, with simplicity relations satisfied automatically, and recover Einstein–Cartan gravity with a cosmological constant and the Holst term.
Finally, we discuss how matter ansätz express spinorial differential forms in terms of spin-1/2 fields. We examine the supersymmetry transformations that preserve these ansätz and explain why these lead to the twistor-spinor equation.
Based on: [arXiv:2608.17900], [arXiv:2601.19734] and [arXiv:2111.09845].