Entanglement versus entwinement in symmetric product orbifolds
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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.
KeywordsAdS-CFT Correspondence Conformal Field Theory Field Theories in Lower Dimensions Gauge Symmetry
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- J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
- S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
- J. Schliemann, D. Loss and A.H. MacDonald, Double-occupancy errors, adiabaticity, and entanglement of spin qubits in quantum dots, Phys. Rev. B 63 (2001) 085311 [cond-mat/0009083].
- J. Schliemann, J.I. Cirac, M. Kus, M. Lewenstein and D. Loss, Quantum correlations in two-fermion systems, Phys. Rev. A 64 (2001) 022303.Google Scholar
- R. Paškauskas and L. You, Quantum correlations in two-boson wave functions, Phys. Rev. A 64 (2001) 042310 [quant-ph/0106117].
- K. Eckert, J. Schliemann, D. Bruß and M. Lewenstein, Quantum correlations in systems of indistinguishable particles, Annals Phys. 299 (2002) 88 [quant-ph/0203060].
- P. Lévay, S. Nagy and J. Pipek, Elementary formula for entanglement entropies of fermionic systems, Phys. Rev. A 72 (2005) 022302 [quant-ph/0501145].
- P. Lévay and P. Vrana, Three fermions with six single-particle states can be entangled in two inequivalent ways, Phys. Rev. A 78 (2008) 022329 [arXiv:0806.4076].
- G. Sárosi and P. Lévay, Coffman-kundu-wootters inequality for fermions, Phys. Rev. A 90 (2014) 052303 [arXiv:1408.6735].
- L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on Orbifolds, Nucl. Phys. B 261 (1985) 678 [INSPIRE].
- P. Di Francesco, P. Mathieu and D. Senechal, Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York (1997) [DOI: https://doi.org/10.1007/978-1-4612-2256-9].