Remarks on Quantum Aspects of 3D-Gravity in the First-Order Formalism

AbstractIn this paper, we reassess the issue of working out the propagatorsand identifying the spectrum of excitations associated to the vielbein andspin connection of (1+2)-D gravity in the presence of torsion by adopt-ing the first-order formulation. A number of peculiarities is pointed outwhenever the Chern-Simons term is taken into account along with thepossible bilinear terms in the torsion tensor. We present a procedure toderive the full set of propagators, based on a set of spin-type operators,and we discuss under which conditions the pole of these tree-level 2-pointfunctions correspond to physical excitations. 1 Introduction The need to better understand gauge fields has lead to an widespread use oflocal transformations due the natural manner gauge fields appear in it. In theattempt to write (1+2)-D gravity as a gauge theory, the formulation requiressome specific technicalities, by virtue of the possibility of including the so-called(topological) Chern-Simons term. Adopting the Poincar´e group as the localgauge group, one naturally obtains the curvature and torsion tensor by means ofthe Cartan´s structure equations. The translational part of the Poincar´e groupis represented by the vielbein gauge fields, e