Fermions on curved backgrounds of matrix models

TL;DR

This paper investigates how fermions propagate on curved branes within matrix models, revealing that their behavior aligns with Einstein-Cartan theory and highlighting the role of torsion in such backgrounds.

Contribution

It provides a detailed analysis of fermion coupling to curved backgrounds in IKKT matrix models, connecting the Dirac operator to torsion-inclusive geometries.

Findings

Fermion propagation matches Einstein-Cartan theory predictions.

Results show an extra coupling to torsion's antisymmetric part.

Analysis includes FLRW cosmological backgrounds.

Abstract

We discuss the propagation of fermions on generic, curved branes in IKKT-type matrix models. The Dirac operator can be understood either in terms of a Weitzenb\"ock connection, or in terms of the Levi-Civita connection with extra torsion term. We discuss in detail the coupling of spin to the background geometry using the JWKB approximation. Despite the absence of local Lorentz invariance in the underlying IKKT framework, our results agree with the expectations of Einstein-Cartan theory, and differ from general relativity only by an extra coupling to the totally antisymmetric part of the torsion. The case of FLRW cosmic background solutions is discussed as a special case.