Fermions Coupled to Emergent Noncommutative Gravity

TL;DR

This paper explores how fermions couple to emergent noncommutative gravity within matrix models, revealing that integrating out fermions induces Einstein-Hilbert action and explains UV/IR mixing as a gravity-related phenomenon.

Contribution

It demonstrates the appropriate coupling of fermions to emergent noncommutative gravity and explains UV/IR mixing through gravitational effects in matrix models.

Findings

Fermion coupling induces Einstein-Hilbert action in noncommutative geometry.

UV/IR mixing is explained as a gravity effect.

Supersymmetry, especially N=4, suppresses UV/IR mixing.

Abstract

We study the coupling of fermions to Yang-Mills matrix models in the framework of emergent noncommutative gravity. It is shown that the matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin-connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action for on-shell geometries plus a dilaton-like term. This result explains UV/IR mixing as a gravity effect. It also illuminates why UV/IR mixing remains even in supersymmetric models, except in the N=4 case.