Abstract
We consider Lifshitz field theories with a dynamical critical exponent z equal to the dimension of space d and with a large group of base space symmetries, concretely space coordinate transformations with unit determinant (“Special Diffeomorphisms”). The field configurations of the theories considered may have the topology of skyrmions, vortices or monopoles, although we focus our detailed investigations on skyrmions. The resulting Lifshitz field theories have a BPS bound and exact soliton solutions saturating the bound, as well as time-dependent topological Q-ball solutions. Finally, we investigate the U(1) gauged versions of the Lifshitz field theories coupled to a Chern-Simons gauge field, where the BPS bound and soliton solutions saturating the bound continue to exist.
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References
E. Lifshitz, On the theory of second-order phase transitions I & II, Zh. Eksp. Teor. Fiz. 11 (1941) 255.
J.A. Hertz, Quantum critical phenomena, Phys. Rev. B 14 (1976) 1165 [INSPIRE].
P. Hořava, Quantum Criticality and Yang-Mills Gauge Theory, Phys. Lett. B 694 (2010) 172 [arXiv:0811.2217] [INSPIRE].
P. Hořava, Quantum Gravity at a Lifshitz Point, Phys. Rev. D 79 (2009) 084008 [arXiv:0901.3775] [INSPIRE].
T. Griffin, P. Hořava and C.M. Melby-Thompson, Lifshitz Gravity for Lifshitz Holography, arXiv:1211.4872 [INSPIRE].
D. Tong and K. Wong, Fluctuation and Dissipation at a Quantum Critical Point, arXiv:1210.1580 [INSPIRE].
D. Blas, M.M. Ivanov and S. Sibiryakov, Testing Lorentz invariance of dark matter, JCAP 10 (2012) 057 [arXiv:1209.0464] [INSPIRE].
E. Barausse and T.P. Sotiriou, A no-go theorem for slowly rotating black holes in Hořava-Lifshitz gravity, Phys. Rev. Lett. 109 (2012) 181101 [Erratum ibid. 110 (2013) 039902] [arXiv:1207.6370] [INSPIRE].
G. Lozano, F.A. Schaposnik and G. Tallarita, Gauged Lifshitz model with Chern-Simons term, arXiv:1210.1182 [INSPIRE].
N. Grandi, I.S. Landea and G.A. Silva, Vortex solutions of the Lifshitz- Chern-Simons theory, Phys. Rev. D 87 (2013) 025031 [arXiv:1206.0611] [INSPIRE].
A. Kobakhidze, J.E. Thompson and R.R. Volkas, BPS solitons in Lifshitz field theories, Phys. Rev. D 83 (2011) 025007 [arXiv:1010.1068] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, A Skyrme-type proposal for baryonic matter, Phys. Lett. B 691 (2010) 105 [arXiv:1001.4544] [INSPIRE].
C. Adam, J. Sanchez-Guillen and A. Wereszczynski, A BPS Skyrme model and baryons at large-N c, Phys. Rev. D 82 (2010) 085015 [arXiv:1007.1567] [INSPIRE].
E. Bonenfant and L. Marleau, Nuclei as near BPS-Skyrmions, Phys. Rev. D 82 (2010) 054023 [arXiv:1007.1396] [INSPIRE].
E. Bonenfant, L. Harbour and L. Marleau, Near-BPS Skyrmions: non-shell configurations and Coulomb effects, Phys. Rev. D 85 (2012) 114045 [arXiv:1205.1414] [INSPIRE].
C. Adam, C. Fosco, J. Queiruga, J. Sanchez-Guillen and A. Wereszczynski, Symmetries and exact solutions of the BPS Skyrme model, arXiv:1210.7839 [INSPIRE].
T. Gisiger and M.B. Paranjape, Solitons in a baby Skyrme model with invariance under volume/area preserving diffeomorphisms, Phys. Rev. D 55 (1997) 7731 [hep-ph/9606328] [INSPIRE].
C. Adam, T. Romanczukiewicz, J. Sanchez-Guillen and A. Wereszczynski, Investigation of restricted baby Skyrme models, Phys. Rev. D 81 (2010) 085007 [arXiv:1002.0851] [INSPIRE].
J.M. Speight, Compactons and semi-compactons in the extreme baby Skyrme model, J. Phys. A 43 (2010) 405201 [arXiv:1006.3754] [INSPIRE].
C. Adam, C. Naya, J. Sanchez-Guillen and A. Wereszczynski, The gauged BPS baby Skyrme model, Phys. Rev. D 86 (2012) 045010 [arXiv:1205.1532] [INSPIRE].
C. Adam, C. Naya, J. Sanchez-Guillen and A. Wereszczynski, A gauged baby Skyrme model and a novel BPS bound, J. Phys. Conf. Ser. 410 (2013) 012055 [arXiv:1209.5103] [INSPIRE].
C. Adam, J. Sanchez-Guillen, A. Wereszczynski and W. Zakrzewski, Topological duality between vortices and planar skyrmions in BPS theories with APD symmetries, Phys. Rev. D 87 (2013) 027703 [arXiv:1209.5403] [INSPIRE].
K. Skenderis and P.K. Townsend, Gravitational stability and renormalization group flow, Phys. Lett. B 468 (1999) 46 [hep-th/9909070] [INSPIRE].
O. DeWolfe, D.Z. Freedman, S.S. Gubser and A. Karch, Modeling the fifth-dimension with scalars and gravity, Phys. Rev. D 62 (2000) 046008 [hep-th/9909134] [INSPIRE].
D.Z. Freedman, C. Núñez, M. Schnabl and K. Skenderis, Fake supergravity and domain wall stability, Phys. Rev. D 69 (2004) 104027 [hep-th/0312055] [INSPIRE].
D. Bazeia, J.D. Dantas, A.R. Gomes, L. Losano and R. Menezes, Twinlike Models in Scalar Field Theories, Phys. Rev. D 84 (2011) 045010 [arXiv:1105.5111] [INSPIRE].
K. Skenderis and P.K. Townsend, Hidden supersymmetry of domain walls and cosmologies, Phys. Rev. Lett. 96 (2006) 191301 [hep-th/0602260] [INSPIRE].
D. Bazeia, C.B. Gomes, L. Losano and R. Menezes, First-order formalism and dark energy, Phys. Lett. B 633 (2006) 415 [astro-ph/0512197] [INSPIRE].
K. Skenderis and P. Townsend, Pseudo-Supersymmetry and the Domain-Wall/Cosmology Correspondence, J. Phys. A 40 (2007) 6733 [hep-th/0610253] [INSPIRE].
A. Ceresole and G. Dall’Agata, Flow Equations for Non-BPS Extremal Black Holes, JHEP 03 (2007) 110 [hep-th/0702088] [INSPIRE].
J. Perz, P. Smyth, T. Van Riet and B. Vercnocke, First-order flow equations for extremal and non-extremal black holes, JHEP 03 (2009) 150 [arXiv:0810.1528] [INSPIRE].
L. Andrianopoli, R. D’Auria, E. Orazi and M. Trigiante, First Order Description of D = 4 static Black Holes and the Hamilton-Jacobi equation, Nucl. Phys. B 833 (2010) 1 [arXiv:0905.3938] [INSPIRE].
L. Andrianopoli, R. D’Auria, S. Ferrara and M. Trigiante, Fake Superpotential for Large and Small Extremal Black Holes, JHEP 08 (2010) 126 [arXiv:1002.4340] [INSPIRE].
G. Dall’Agata, Black holes in supergravity: flow equations and duality, arXiv:1106.2611 [INSPIRE].
M. Trigiante, T. Van Riet and B. Vercnocke, Fake supersymmetry versus Hamilton-Jacobi, JHEP 05 (2012) 078 [arXiv:1203.3194] [INSPIRE].
D. Bazeia and J. Dantas, On the presence of twinlike models in cosmology, Phys. Rev. D 85 (2012) 067303 [arXiv:1202.5978] [INSPIRE].
I. Bakas, F. Bourliot, D. Lüst and M. Petropoulos, Geometric Flows in Hořava-Lifshitz Gravity, JHEP 04 (2010) 131 [arXiv:1002.0062] [INSPIRE].
I. Bakas, Gradient flows and instantons at a Lifshitz point, J. Phys. Conf. Ser. 283 (2011) 012004 [arXiv:1009.6173] [INSPIRE].
O. Alvarez, L.A. Ferreira and J. Sanchez Guillen, A New approach to integrable theories in any dimension, Nucl. Phys. B 529 (1998) 689 [hep-th/9710147] [INSPIRE].
O. Alvarez, L. Ferreira and J. Sanchez-Guillen, Integrable theories and loop spaces: fundamentals, applications and new developments, Int. J. Mod. Phys. A 24 (2009) 1825 [arXiv:0901.1654] [INSPIRE].
B.M.A.G. Piette, B.J. Schroers and W.J. Zakrzewski, Multi-solitons in a two-dimensional Skyrme model, Z. Phys. C 65 (1995) 165 [hep-th/9406160] [INSPIRE].
B.M.A.G. Piette, B.J. Schroers and W.J. Zakrzewski, Dynamics of baby skyrmions, Nucl. Phys. B 439 (1995) 205 [hep-ph/9410256] [INSPIRE].
P. Klimas and N. Sawado, Numerical vortex solutions in (3 + 1) dimensions for the extended CP N Skyrme-Faddeev model, arXiv:1210.7523 [INSPIRE].
R.A. Leese, M. Peyrard and W.J. Zakrzewski, Soliton scatterings in some relativistic models in (2 + 1) dimensions, Nonlinearity 3 (1990) 773.
B.M.A.G. Piette and W.J. Zakrzewski, Skyrmion dynamics in (2 + 1) dimensions, Chaos, Solitons and Fractals 5 (1995) 2495.
P.M. Sutcliffe, The interaction of Skyrme-like lumps in (2+1) dimensions, Nonlinearity 4 (1991) 1109.
T. Weidig, The baby Skyrme models and their multi-skyrmions, Nonlinearity 12 (1999) 1489.
P. Eslami, M. Sarbishaei and W.J. Zakrzewski, Baby Skyrme models for a class of potentials, Nonlinearity 13 (2000) 1867.
A.E. Kudryavtsev, B. Piette and W. Zakrzewski, Mesons, baryons and waves in the baby Skyrmion model, Eur. Phys. J. C 1 (1998) 333 [hep-th/9611217] [INSPIRE].
M. Karliner and I. Hen, Rotational symmetry breaking in baby Skyrme models, Nonlinearity 21 (2008) 399.
M. Karliner and I. Hen, Review of Rotational Symmetry Breaking in Baby Skyrme Models, arXiv:0901.1489 [INSPIRE].
J. Jaykka, M. Speight and P. Sutcliffe, Broken Baby Skyrmions, Proc. Roy. Soc. Lond. A 468 (2012) 1085 [arXiv:1106.1125] [INSPIRE].
J. Jaykka and M. Speight, Easy plane baby skyrmions, Phys. Rev. D 82 (2010) 125030 [arXiv:1010.2217] [INSPIRE].
D. Foster, Baby Skyrmion chains, Nonlinearity 23 (2010) 465.
C. Adam, P. Klimas, J. Sanchez-Guillen and A. Wereszczynski, Compact baby skyrmions, Phys. Rev. D 80 (2009) 105013 [arXiv:0909.2505] [INSPIRE].
C.K. Zachos, D. Fairlie and T. Curtright, Matrix membranes and integrability, Lect. Notes Phys. 502 (1998) 183 [hep-th/9709042] [INSPIRE].
T. Curtright, D. Fairlie and C.K. Zachos, Integrable symplectic trilinear interaction terms for matrix membranes, Phys. Lett. B 405 (1997) 37 [hep-th/9704037] [INSPIRE].
A.S. Dutra and R. Correa, On the Behavior of Oscillons and Breathers in Lorentz Violating Scenarios, arXiv:1212.4448 [INSPIRE].
B. Schroers, Bogomolny solitons in a gauged O(3) σ-model, Phys. Lett. B 356 (1995) 291 [hep-th/9506004] [INSPIRE].
H. Aratyn, L. Ferreira and A. Zimerman, Exact static soliton solutions of (3 + 1)-dimensional integrable theory with nonzero Hopf numbers, Phys. Rev. Lett. 83 (1999) 1723 [hep-th/9905079] [INSPIRE].
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ArXiv ePrint: 1212.2741
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Adam, C., Naya, C., Sanchez-Guillen, J. et al. Lifshitz field theories with SDiff symmetries. J. High Energ. Phys. 2013, 12 (2013). https://doi.org/10.1007/JHEP03(2013)012
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DOI: https://doi.org/10.1007/JHEP03(2013)012