178 research outputs found
Noncommutative Geometric Spaces with Boundary: Spectral Action
We study spectral action for Riemannian manifolds with boundary, and then
generalize this to noncommutative spaces which are products of a Riemannian
manifold times a finite space. We determine the boundary conditions consistent
with the hermiticity of the Dirac operator. We then define spectral triples of
noncommutative spaces with boundary. In particular we evaluate the spectral
action corresponding to the noncommutative space of the standard model and show
that the Einstein-Hilbert action gets modified by the addition of the extrinsic
curvature terms with the right sign and coefficient necessary for consistency
of the Hamiltonian. We also include effects due to the addition of dilaton
field.Comment: 26 page
Remarks on the Spectral Action Principle
The presence of chiral fermions in the physical Hilbert space implies
consistency conditions on the spectral action. These conditions are equivalent
to the absence of gauge and gravitational anomalies. Suggestions for the
fermionic part of the spectral action are made based on the supersymmetrisation
of the bosonic part.Comment: 10 pages, Latex fil
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