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We revisit the calculation of multi-interval modular Hamiltonians for freefermions using a Euclidean path integral approach. We show how themulti-interval modular flow is obtained by gluing together the single intervalmodular flows. Using this relation, we obtain an exact expression for themulti-interval modular Hamiltonian and entanglement entropy in agreement withexisting results. An essential ingredient in our derivation is the introductionof the \emp{modular action}. This determines the non-local field theorydescribing the free fermion reduced density matrix, and makes manifest it'snon-local conformal symmetry and $U(1)$ Kacs-Moody symmetry.

Gluing together Modular flows with free fermions