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Splitting of folded strings in AdS 4×CP 3

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Abstract

We study classically splitting of two kinds of folded string solution in AdS 4×CP 3. Conserved charges of the produced fragments are computed for each case. We find interesting patterns among these conserved charges.

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Notes

  1. Some discussions on non-planar sector via other approaches appeared in [32–35].

  2. The energy and the Noether charges from the Cartan generators of SU(4) before splitting have already been computed in [36].

  3. They are listed in the Appendix.

  4. We choose the normalization of J such that \(J^{\mu}_{\,\,\nu } J^{\nu}_{\,\,\rho}=-\delta^{\mu}_{\rho}\).

  5. Here when ξ<0, we change the coordinates ξ,φ 2 into −ξ,φ 2+2π.

  6. We use E(q),K(q) to denote the elliptic integrals of first kind and second kind, respectively. We use E(q,x) and F(q,x) to denote the corresponding incomplete elliptic integral. Our convention is that E(q,π/2)=E(q),F(q,π/2)=K(q).

  7. Here, as in Sect. 3, when θ 1<0, we change the coordinates θ 1,θ 2,ψ,φ 1,φ 2 into −θ 1,−θ 2,ψ+π,φ 1−π,φ 2+π. We thank the referee for suggestions on this footnote and footnote 5.

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Acknowledgements

JW would like to thank Bin Chen and San-Min Ke for discussions and encouragement. The work of JW is partly supported by NSFC under Grant No. 11105154 by Youth Innovation Promotion Association, CAS.

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Authors and Affiliations

  1. Institute of High Energy Physics, and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, Beijing, 100049, P.R. China

    Jun-Bao Wu

  2. Kavli Institute for Theoretical Physics China, CAS, Beijing, 100190, P.R. China

    Jun-Bao Wu

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  1. Jun-Bao Wu
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Correspondence to Jun-Bao Wu.

Appendix: The generators of SU(4)

Appendix: The generators of SU(4)

Now we list the generators of SU(4) in fundamental representation used in [39] to compute the Killing vectors:

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Wu, JB. Splitting of folded strings in AdS 4×CP 3 . Eur. Phys. J. C 72, 2109 (2012). https://doi.org/10.1140/epjc/s10052-012-2109-8

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