Entanglement versus entwinement in symmetric product orbifolds

Understand

We study the entanglement entropy of gauged internal degrees of freedom in a two dimensional symmetric product orbifold CFT, whose configurations consist of $N$ strands sewn together into "long" strings, with wavefunctions symmetrized under permutations.

• In earlier work a related notion of "entwinement" was introduced.
• Here we treat this system analogously to a system of $N$ identical particles.
• From an algebraic point of view, we point out that the reduced density matrix on $k$ out of $N$ particles is not associated with a subalgebra of operators, but rather with a linear subspace, which we explain is sufficient.