This paper investigates entanglement entropy in $3+1$ dimensional Lorentzian covariant loop quantum gravity (LQG). We compute the entanglement entropy for a spatial region from states dynamically generated by a spinfoam path integral that sums over a family of two-complexes. The resulting entropy exhibits a geometric area law, $S\simeq \beta a$, where the area $a$ of the entangling surface is determined by the LQG area spectrum and the leading coefficient $\beta >0$ is independent of the underlying two-complexes. By relating the coupling constant of the sum over two-complexes to the Barbero-Immirzi parameter $\gamma$, we reproduce the Bekenstein-Hawking formula for the range $0<\gamma \lesssim 1/2$. This work provides a Lorentzian path integral approach to gravitational entropy without the need for contour prescriptions.

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• Loop quantum gravity