TY - JOUR

T1 - Supersymmetric 3D model for gravity with SU(2) gauge symmetry, mass generation and effective cosmological constant

AU - Alvarez, Pedro D.

AU - Pais, Pablo

AU - Rodríguez, Eduardo

AU - Salgado-Rebolledo, Patricio

AU - Zanelli, Jorge

N1 - Publisher Copyright:
© 2015 IOP Publishing Ltd.

PY - 2015/9/10

Y1 - 2015/9/10

N2 - A Chern-Simons system in 2+1 dimensions invariant under local Lorentz rotations, SU(2) gauge transformations, and local supersymmetry (SUSY) transformations is proposed. The field content is that of (2+1)-gravity plus an SU(2) gauge field, a spin-1/2 fermion charged with respect to SU(2) and a trivial free abelian gauge field. A peculiarity of the model is the absence of gravitini, although it includes gravity and SUSY. Likewise, no gauginos are present. All the parameters involved in the system are either protected by gauge invariance or emerge as integration constants. An effective mass and effective cosmological constant emerge by spontaneous breaking of local scaling invariance. The vacuum sector is defined by configurations with locally flat Lorentz and SU(2) connections sporting nontrivial global charges. Three-dimensional Lorentz-flat geometries are spacetimes of locally constant negative - or zero - Riemann curvature, which include Minkowski space, AdS3, BTZ black holes, and point particles. These solutions admit different numbers of globally defined, covariantly constant spinors and are therefore good candidates for stable ground states. The fermionic sector in this system could describe the dynamics of electrons in graphene in the long wavelength limit near the Dirac points, with the spin degree of freedom of the electrons represented by the SU(2) label. If this is the case, the SU(2) gauge field would produce a spin-spin interaction giving rise to strong correlation of electron pairs.

AB - A Chern-Simons system in 2+1 dimensions invariant under local Lorentz rotations, SU(2) gauge transformations, and local supersymmetry (SUSY) transformations is proposed. The field content is that of (2+1)-gravity plus an SU(2) gauge field, a spin-1/2 fermion charged with respect to SU(2) and a trivial free abelian gauge field. A peculiarity of the model is the absence of gravitini, although it includes gravity and SUSY. Likewise, no gauginos are present. All the parameters involved in the system are either protected by gauge invariance or emerge as integration constants. An effective mass and effective cosmological constant emerge by spontaneous breaking of local scaling invariance. The vacuum sector is defined by configurations with locally flat Lorentz and SU(2) connections sporting nontrivial global charges. Three-dimensional Lorentz-flat geometries are spacetimes of locally constant negative - or zero - Riemann curvature, which include Minkowski space, AdS3, BTZ black holes, and point particles. These solutions admit different numbers of globally defined, covariantly constant spinors and are therefore good candidates for stable ground states. The fermionic sector in this system could describe the dynamics of electrons in graphene in the long wavelength limit near the Dirac points, with the spin degree of freedom of the electrons represented by the SU(2) label. If this is the case, the SU(2) gauge field would produce a spin-spin interaction giving rise to strong correlation of electron pairs.

KW - ChernSimons

KW - Weyl symmetry

KW - grapheme

KW - gravity

KW - supersymmetry

UR - http://www.scopus.com/inward/record.url?scp=84939607102&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/32/17/175014

DO - 10.1088/0264-9381/32/17/175014

M3 - Article

AN - SCOPUS:84939607102

SN - 0264-9381

VL - 32

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 17

M1 - 175014

ER -