Supergravity on the noncommutative geometry

Abstract

Two years ago, we found the supersymmetric counterpart of the spectral triple which specified noncommutative geometry. Based on the triple, we derived gauge vector supermultiplets, Higgs supermultiplets of the minimum supersymmetric standard model and its action. However, unlike the famous theories of Connes and his co-workers, the action does not couple to gravity. In this paper, we obtain the supersymmetric Dirac operator ${\mathcal{D}}_M^{(SG)}$ on the Riemann-Cartan curved space replacing derivatives which appear in that of the triple with the covariant derivatives of general coordinate transformation. We apply the supersymmetric version of the spectral action principle and investigate the heat kernel expansion on the square of the Dirac operator. As a result, we obtain a new supergravity action which does not include the Ricci curvature tensor.

arXiv commentto be published in "Progress of Theoretical and Experimental Physics"

References in corpus (13)

• A Supersymmetry Primer
• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• Gravity and the standard model with neutrino mixing
• A Universal Action Formula
• Noncommutative Geometry and the standard model with neutrino mixing
• Why the Standard Model
• Conformal Quantum Gravity with the Gauss-Bonnet Term
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• The Path Integral for a Particle in Curved Spaces and Weyl Anomalies
• Minimum Supersymmetric Standard Model on the Noncommutative Geometry
• Supersymmetric Dirac Operator on the Noncommutative Geometry
• Supersymmetric Yang-Mills Theory on the Noncommutative Geometry