TY - JOUR

T1 - Abelian Hopfions of the CPn model on R2n+1 and a fractionally powered topological lower bound

AU - Radu, Eugen

AU - Tchrakian, D. H.

AU - Yang, Yisong

N1 - Funding Information:
This work was started as part of project RFP07-PHY of Science Foundation Ireland (SFI) . E.R. gratefully acknowledge support by the DFG , in particular, also within the DFG Research Training Group 1620 “Models of Gravity”. E.R. and D.H.T. would like to thank David Foster for collaboration on the issue of numerical Hopfions in dimensions, and are also grateful to Olaf Lechtenfeld, Yasha Shnir, Paul Sutcliffe and especially Mikhail Volkov for valuable discussions.

PY - 2013/10/11

Y1 - 2013/10/11

N2 - Regarding the Skyrme-Faddeev model on R3 as a CP1 sigma model, we propose CPn sigma models on R2n+1 as generalisations which may support finite energy Hopfion solutions in these dimensions. The topological charge stabilising these field configurations is the Chern-Simons charge, namely the volume integral of the Chern-Simons density which has a local expression in terms of the composite connection and curvature of the CPn field. It turns out that subject to the sigma model constraint, this density is a total divergence. We prove the existence of a topological lower bound on the energy, which, as in the Vakulenko-Kapitansky case in R3, is a fractional power of the topological charge, depending on n. The numerical construction of the simplest ring shaped un-knot Hopfion on R5 is also discussed.

AB - Regarding the Skyrme-Faddeev model on R3 as a CP1 sigma model, we propose CPn sigma models on R2n+1 as generalisations which may support finite energy Hopfion solutions in these dimensions. The topological charge stabilising these field configurations is the Chern-Simons charge, namely the volume integral of the Chern-Simons density which has a local expression in terms of the composite connection and curvature of the CPn field. It turns out that subject to the sigma model constraint, this density is a total divergence. We prove the existence of a topological lower bound on the energy, which, as in the Vakulenko-Kapitansky case in R3, is a fractional power of the topological charge, depending on n. The numerical construction of the simplest ring shaped un-knot Hopfion on R5 is also discussed.

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U2 - 10.1016/j.nuclphysb.2013.07.006

DO - 10.1016/j.nuclphysb.2013.07.006

M3 - Article

AN - SCOPUS:84881541825

VL - 875

SP - 388

EP - 407

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 2

ER -