In this talk, I consider the propagation of fermions on generic, curved backgrounds of the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) matrix model. I discuss the coupling of spin to the background geometry using the Jeffreys-Wentzel-Kramers-Brillouin (JWKB) approximation. Despite the absence of local Lorentz invariance in the underlying IKKT framework, the obtained 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 Friedmann-Lemaître-Robertson-Walker cosmic background solutions is briefly considered as a special case. The talk is based on:

E. Battista and H. Steinacker, “Fermions on curved backgrounds of matrix models”, Phys. Rev. D 107, 046021 (2023).