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2010

BPS solitons in Lifshitz field theories

Kobakhidze, Archil, Thompson, Jayne E., Volkas, Raymond R.

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Lorentz-invariant scalar field theories in d+1 dimensions with second-order derivative terms are unable to support static soliton solutions that are both finite in energy and stable for d>2, a result known as Derrick's theorem.

Lifshitz theories, which introduce higher-order spatial derivatives, need not obey Derrick's theorem.
We construct stable, finite-energy, static soliton solutions in Lifshitz scalar field theories in 3+1 dimensions with dynamical critical exponent z=2.
We exhibit three generic types: non-topological point defects, topological point defects, and topological strings.

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P. Hořava, Phys. Rev. D79, 084008 (2009) [arXiv:0901.3775]; JHEP 03, 020 (2009) [arXiv:0812.4287]; Phys. Rev. Lett. 102, 161301 (2009) [arXiv:0902.3657]
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R. Iengo, J. G. Russo and M. Serone, JHEP 0911, 020 (2009) [arXiv:0906.3477]; R. Iengo, and M. Serone, Phys. Rev. D81, 125005 (2010) [arXiv:1003.4430]; D. Anselmi, Annals Phys. 324, 874 (2009) [arXiv:0808.3470]; ibid
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P. Hořava and C. M. Melby-Thompson, [arXiv:1007.3657]
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Then

P. Hořava, Phys. Lett. B 694
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R. Dijkgraaf, D. Orlando and S. Reffert, Nucl. Phys. B824, 365 (2010) [arXiv:0903.0732]; D. Orlando and S. Reffert, Class. Quant. Grav. 26, 155021 (2009) [arXiv:0905.0301]; D.Orlando and S. Reffert, Phys. Lett. B 683, 62 (2010) [arXiv:0908.4429 ]; I. Bakas, [arXiv:1009.6173]
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2010
Closest in time.
J. E. Thompson and R. R. Volkas, [arXiv:1008.2054]
Original
2054
Closest in time.

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