Paper detail

Supergravity with Lagrange Multiplier Fields in 2 + 1 Dimensions

We examine the first-order Einstein-Cartan (EC) action in 2+1 dimensions, including a cosmological term and its supersymmetric extension. In this setting the spin connection can be expressed as an axial vector, yielding an action that is bilinear in the quantum fields and allows quantization without background fields. We identify the complete set of first-class constraints and derive the associated gauge transformations, which differ from the standard diffeomorphism and local Lorentz invariances. Using the closed gauge algebra, we construct the Faddeev-Popov-Nielsen path integral and show how a Lagrange multiplier field can be introduced to remove higher-loop contributions while preserving unitarity and gauge invariance.