# The Quantum Theory of Chern-Simons Supergravity

## TL;DR

This paper explores the quantization of $AdS_3$ $N$-extended Chern-Simons supergravity, analyzing gauge symmetries, BRST symmetry, and gauge-fixing, revealing connections to graphene fermion models.

## Contribution

It introduces a BRST quantization framework for $AdS_3$ supergravity and links specific gauge-fixings to models of graphene fermions.

## Key findings

- Different gauge-fixings lead to distinct quantum features.
- A particular gauge-fixing reproduces the graphene fermion Ansatz.
- The quantization approach clarifies the gauge symmetry structure.

## 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.