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arXiv · 1806.02871

Entanglement versus entwinement in symmetric product orbifolds

Vijay Balasubramanian·Ben Craps·Tim De Jonckheere·Gábor Sárosi
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Abstract

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. In the orbifold CFT, we compute the entropy of a single strand in states holographically dual in the D1/D5 system to a conical defect geometry or a massless BTZ black hole and find a result identical to entwinement. We also calculate the entropy of two strands in the state that represents the conical defect; the result differs from entwinement. In this case, matching entwinement would require finding a gauge-invariant way to impose continuity across strands.

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Vijay Balasubramanian, Ben Craps, Tim De Jonckheere, Gábor Sárosi. 2018-06-07. Entanglement versus entwinement in symmetric product orbifolds. https://doi.org/10.1007/jhep01(2019)190

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