Fermions on curved backgrounds of matrix models

We discuss the propagation of fermions on generic, curved branes in Ishibashi-Kawai-Kitazawa-Tsuchiya-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 an extra torsion term. We discuss in detail the coupling of spin to the background geometry using the Jeffreys-Wentzel-Kramers-Brillouin approximation. Despite the absence of local Lorentz invariance in the underlying Ishibashi-Kawai-Kitazawa-Tsuchiya 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 Friedmann–-Lema\^{\i}tre-–Robertson-–Walker cosmic background solutions is discussed as a special case.

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