The Holst Action by the Spectral Action Principle
  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. 
Frank Pfaeffle and Christoph A. Stephan
math-ph gr-qc math.MP