Spectral action beyond the weak-field approximation

Abstract

The spectral action for a non-compact commutative spectral triple is computed covariantly in a gauge perturbation up to order 2 in full generality. In the ultraviolet regime, $p\to \infty$, the action decays as $1/p^4$ in any even dimension.

17 pages Few misprints corrected

References in corpus (4)

• Inner fluctuations of the spectral action
• Bosonic Spectral Action Induced from Anomaly Cancelation
• Renormalization of the asymptotically expanded Yang-Mills spectral action
• An integer-valued version of the Birman-Krein formula

Cited by in corpus (16)

• On the non-local heat kernel expansion
• High energy bosons do not propagate
• Quantum Gravity signatures in the Unruh effect
• Wick Rotation and Fermion Doubling in Noncommutative Geometry
• Renormalization of the asymptotically expanded Yang-Mills spectral action
• Spectral dimensions from the spectral action
• Spectral action with zeta function regularization
• Diagram technique for the heat kernel of the covariant Laplace operator
• Heat-kernel approach for scattering
• Asymptotic and exact expansions of heat traces
• Spectral Noncommutative Geometry, Standard Model and all that
• Reflection positivity in higher derivative scalar theories
• Unification of Coupling Constants, Dimension six Operators and the Spectral Action
• One-loop corrections to the spectral action
• Can Spectral Action be a Window to Very High Energies?
• Higher-derivative gauge theories from noncommutative geometry