The Quantum Theory of Chern-Simons Supergravity

Abstract: We consider $AdS_3$ $N$-extended Chern-Simons supergravity (`a la Achucarro-Tonswend) and we study its gauge symmetries. We promote those gauge symmetries to a BRST symmetry and we perform its quantization by choosing suitable gauge-fixings. The resulting quantum theories have different features which we discuss in the present work. In particular, we show that a special choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez, Valenzuela and Zanelli for the graphene fermion.