Journal of High Energy Physics

, 2019:190 | Cite as

Entanglement versus entwinement in symmetric product orbifolds

  • Vijay Balasubramanian
  • Ben Craps
  • Tim De Jonckheere
  • Gábor SárosiEmail author
Open Access
Regular Article - Theoretical Physics


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.


AdS-CFT Correspondence Conformal Field Theory Field Theories in Lower Dimensions Gauge Symmetry 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.David Rittenhouse LaboratoryUniversity of PennsylvaniaPhiladelphiaU.S.A.
  2. 2.Theoretische Natuurkunde, Vrije Universiteit Brussel, and International Solvay InstitutesBrusselsBelgium

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