Unconventional Supersymmetry at the Boundary of AdS_4 Supergravity

TL;DR

This paper explores a boundary theory derived from N=2 AdS_4 supergravity, revealing an unconventional supersymmetric model relevant for condensed matter systems like graphene.

Contribution

It demonstrates how to obtain a D=3 super-Chern-Simons theory with unconventional supersymmetry from a specific asymptotic limit of D=4 supergravity.

Findings

Boundary theory has OSp(2|2) x SO(1,2) invariance

Reproduces the model with specific parameter prescriptions

Dirac fermion arises from radial gravitini components

Abstract

In this paper we perform, in the spirit of the holographic correspondence, a particular asymptotic limit of N=2, AdS_4 supergravity to N=2 supergravity on a locally AdS_3 boundary. Our boundary theory enjoys OSp(2|2) x SO(1,2) invariance and is shown to contain the D=3 super-Chern Simons OSp(2|2) theory considered in [Alvarez:2011gd] and featuring "unconventional local supersymmetry". The model constructed in that reference describes the dynamics of a spin-1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to be relevant for the description of graphene, near the Dirac points, for specific spatial geometries. Our construction yields the model in [Alvarez:2011gd] with a specific prescription on the parameters. In this framework the Dirac spin-1/2 fermion originates from the radial components of the gravitini in D=4.