Fermions and Emergent Noncommutative Gravity

TL;DR

This paper demonstrates how fermions coupled to Yang-Mills matrix models can lead to emergent gravity, reproducing Einstein-Hilbert action and explaining UV/IR mixing phenomena in noncommutative gauge theories.

Contribution

It introduces a matrix model framework for fermions coupled to gravity, revealing how integrating out fermions induces gravitational actions and clarifies UV/IR mixing effects.

Findings

Induces Einstein-Hilbert action from fermion integration

Explains UV/IR mixing in noncommutative gauge theories

Shows differences in UV/IR mixing across supersymmetric models

Abstract

Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple 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 and a dilaton-like term, at least for on-shell geometries. This explains and precisely reproduces the UV/IR mixing for fermions in noncommutative gauge theory, extending recent results for scalar fields. It also explains why some UV/IR mixing remains even in supersymmetric models, except in the N=4 case.