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 D = 5 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 -