9 research outputs found
Renormalization of the asymptotically expanded Yang-Mills spectral action
We study renormalizability aspects of the spectral action for the Yang-Mills
system on a flat 4-dimensional background manifold, focusing on its asymptotic
expansion. Interpreting the latter as a higher-derivative gauge theory, a
power-counting argument shows that it is superrenormalizable. We determine the
counterterms at one-loop using zeta function regularization in a background
field gauge and establish their gauge invariance. Consequently, the
corresponding field theory can be renormalized by a simple shift of the
spectral function appearing in the spectral action.
This manuscript provides more details than the shorter companion paper, where
we have used a (formal) quantum action principle to arrive at gauge invariance
of the counterterms. Here, we give in addition an explicit expression for the
gauge propagator and compare to recent results in the literature.Comment: 28 pages; revised version. To appear in CMP. arXiv admin note:
substantial text overlap with arXiv:1101.480