One-loop corrections to the spectral action

Abstract

We analyze the perturbative quantization of the spectral action in noncommutative geometry and establish its one-loop renormalizability in a generalized sense, while staying within the spectral framework of noncommutative geometry. Our result is based on the perturbative expansion of the spectral action in terms of higher Yang-Mills and Chern-Simons forms. In the spirit of random noncommutative geometries, we consider the path integral over matrix fluctuations around a fixed noncommutative gauge background and show that the corresponding one-loop counterterms are of the same form so that they can be safely subtracted from the spectral action. A crucial role will be played by the appropriate Ward identities, allowing for a fully spectral formulation of the quantum theory at one loop.

15 pages; minor corrections made

References in corpus (4)

• Inner fluctuations of the spectral action
• Quanta of Geometry: Noncommutative Aspects
• Spectral dimensions from the spectral action
• Renormalization of the spectral action for the Yang-Mills system

Cited by in corpus (2)

• Octonion Internal Space Algebra for the Standard Model
• From Noncommutative Geometry to Random Matrix Theory