Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions

Abstract

We study fermions coupled to Yang-Mills matrix models from the point of view of emergent gravity. The matrix model Dirac operator provides an appropriate coupling for fermions to the effective gravitational metric for general branes with nontrivial embedding, albeit with a non-standard spin connection. This generalizes previous results for 4-dimensional matrix models. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the Poisson tensor to the Riemann tensor, and a dilaton-like term.

34 pages; minor changes

References in corpus (5)

• Emergent Gravity from Noncommutative Spacetime
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• Emergent Gravity, Matrix Models and UV/IR Mixing
• Cosmological solutions of emergent noncommutative gravity
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Cited by in corpus (6)

• Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model
• Gauge Theories on Deformed Spaces
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• Curvature and Gravity Actions for Matrix Models
• Heat kernel expansion and induced action for the matrix model Dirac operator
• Heat kernel expansion and induced action for matrix models