TY - JOUR
T1 - A higher-order Skyrme model
AU - Gudnason, Sven Bjarke
AU - Nitta, Muneto
N1 - Funding Information:
We thank Martin Speight for useful discussions. S. B. G. thanks the Recruitment Program of High-end Foreign Experts for support. The work of S. B. G. was supported by the National Natural Science Foundation of China (Grant No. 11675223). The work of M. N. is supported in part by a Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” (KAKENHI Grant No. 15H05855) from the Ministry of Education, Culture, Sports, Science (MEXT) of Japan, by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (KAKENHI Grant No. 16H03984) and by the MEXT-Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006).
Publisher Copyright:
© 2017, The Author(s).
PY - 2017/9/1
Y1 - 2017/9/1
N2 - We propose a higher-order Skyrme model with derivative terms of eighth, tenth and twelfth order. Our construction yields simple and easy-to-interpret higher-order Lagrangians. We first show that a Skyrmion with higher-order terms proposed by Marleau has an instability in the form of a baby-Skyrmion string, while the static energies of our construction are positive definite, implying stability against time-independent perturbations. However., we also find that the Hamiltonians of our construction possess two kinds of dynamical instabilities, which may indicate the instability with respect to time-dependent perturbations. Different from the well-known Ostrogradsky instability, the instabilities that we find are intrinsically of nonlinear nature and also due to the fact that even powers of the inverse metric gives a ghost-like higher-order kinetic-like term. The vacuum state is, however, stable. Finally., we show that at sufficiently low energies, our Hamiltonians in the simplest cases, are stable against time-dependent perturbations.
AB - We propose a higher-order Skyrme model with derivative terms of eighth, tenth and twelfth order. Our construction yields simple and easy-to-interpret higher-order Lagrangians. We first show that a Skyrmion with higher-order terms proposed by Marleau has an instability in the form of a baby-Skyrmion string, while the static energies of our construction are positive definite, implying stability against time-independent perturbations. However., we also find that the Hamiltonians of our construction possess two kinds of dynamical instabilities, which may indicate the instability with respect to time-dependent perturbations. Different from the well-known Ostrogradsky instability, the instabilities that we find are intrinsically of nonlinear nature and also due to the fact that even powers of the inverse metric gives a ghost-like higher-order kinetic-like term. The vacuum state is, however, stable. Finally., we show that at sufficiently low energies, our Hamiltonians in the simplest cases, are stable against time-dependent perturbations.
KW - Effective Field Theories
KW - Sigma Models
KW - Solitons Monopoles and Instantons
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U2 - 10.1007/JHEP09(2017)028
DO - 10.1007/JHEP09(2017)028
M3 - Article
AN - SCOPUS:85029228731
VL - 2017
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 9
M1 - 28
ER -