  We investigate how topological entanglement of Chern-Simons theory is
captured in a string theoretic realization. Our explorations are motivated by a
desire to understand how quantum entanglement of low energy open string degrees
of freedom is encoded in string theory (beyond the oft discussed classical
gravity limit). Concretely, we realize the Chern-Simons theory as the
worldvolume dynamics of topological D-branes in the topological A-model string
theory on a Calabi-Yau target. Via the open/closed topological string duality
one can map this theory onto a pure closed topological A-model string on a
different target space, one which is related to the original Calabi-Yau
geometry by a geometric/conifold transition. We demonstrate how to uplift the
replica construction of Chern-Simons theory directly onto the closed string and
show that it provides a meaningful definition of reduced density matrices in
topological string theory. Furthermore, we argue that the replica construction
commutes with the geometric transition, thereby providing an explicit closed
string dual for computing reduced states, and Renyi and von Neumann entropies
thereof. While most of our analysis is carried out for Chern-Simons on S^3, the
emergent picture is rather general. Specifically, we argue that quantum
entanglement on the open string side is mapped onto quantum entanglement on the
closed string side and briefly comment on the implications of our result for
physical holographic theories where entanglement has been argued to be crucial
ingredient for the emergence of classical geometry.
