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

TL;DR

This paper explores how fermions interact with emergent gravity in Yang-Mills matrix models, showing that integrating out fermions induces Einstein-Hilbert action and additional geometric terms in curved brane backgrounds.

Contribution

It generalizes previous 4D results to curved branes with nontrivial embeddings, revealing how fermions couple to the effective gravitational metric and induce Einstein-Hilbert action.

Findings

Fermions couple to the emergent metric via a matrix model Dirac operator.

Integrating out fermions induces Einstein-Hilbert and additional geometric terms.

The approach extends to curved branes with nontrivial embeddings.

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.