  What is the meaning of entanglement in a theory of extended objects such as
strings? To address this question we consider the spatial entanglement between
two intervals in the Gross-Taylor model, the string theory dual to
two-dimensional Yang-Mills theory at large $N$. The string diagrams that
contribute to the entanglement entropy describe open strings with endpoints
anchored to the entangling surface, as first argued by Susskind. We develop a
canonical theory of these open strings, and describe how closed strings are
divided into open strings at the level of the Hilbert space. We derive the
Modular hamiltonian for the Hartle-Hawking state and show that the
corresponding reduced density matrix describes a thermal ensemble of open
strings ending on an object at the entangling surface that we call an E-brane.
