TY - JOUR
A1 - Pfäffle, Frank
A1 - Stephan, Christoph A.
T1 - Chiral asymmetry and the spectral action
JF - Communications in mathematical physics
N2 - We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.
Y1 - 2013
U6 - http://dx.doi.org/10.1007/s00220-012-1641-6
SN - 0010-3616 (print)
SN - 1432-0916 (online)
VL - 321
IS - 2
SP - 283
EP - 310
PB - Springer
CY - New York
ER -
TY - JOUR
A1 - Pfäffle, Frank
A1 - Stephan, Christoph A.
T1 - On gravity, torsion and the spectral action principle
JF - Journal of functional analysis
N2 - We consider compact Riemannian spin manifolds without boundary equipped with orthogonal connections. We investigate the induced Dirac operators and the associated commutative spectral triples. In case of dimension four and totally anti-symmetric torsion we compute the Chamseddine-Connes spectral action, deduce the equations of motions and discuss critical points.
KW - Orthogonal connections with torsion
KW - Spectral triples
KW - Commutative geometries
KW - Chamseddine-Connes spectral action
Y1 - 2012
U6 - http://dx.doi.org/10.1016/j.jfa.2011.11.013
SN - 0022-1236 (print)
VL - 262
IS - 4
SP - 1529
EP - 1565
PB - Elsevier
CY - San Diego
ER -
TY - JOUR
A1 - Pfäffle, Frank
A1 - Stephan, Christoph A.
T1 - The holst action by the spectral action principle
JF - Communications in mathematical physics
N2 - We investigate the Holst action for closed Riemannian 4-manifolds with orthogonal connections. For connections whose torsion has zero Cartan type component we show that the Holst action can be recovered from the heat asymptotics for the natural Dirac operator acting on left-handed spinor fields.
Y1 - 2011
U6 - http://dx.doi.org/10.1007/s00220-011-1303-0
SN - 0010-3616 (print)
VL - 307
IS - 1
SP - 261
EP - 273
PB - Springer
CY - New York
ER -