TY - JOUR

T1 - Boundary charges and integral identities for solitons in (d + 1)-dimensional field theories

AU - Gudnason, Sven Bjarke

AU - Gao, Zhifeng

AU - Yang, Yisong

N1 - Funding Information:
We thank Ken Konishi for discussion. The work of S.B.G. is supported by the National Natural Science Foundation of China (Grant No. 11675223 ). The work of Z.G. is supported by the National Natural Science Foundation of China (Grant No. U1504102 ). Y.Y. was partially supported by National Natural Science Foundation of China (Grant No. 11471100 ). Appendix A
Publisher Copyright:
© 2017 The Authors

PY - 2017/12

Y1 - 2017/12

N2 - We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions. The construction provides five boundary charges that are related to certain integrals of the profile functions of the solitons in question. The framework is quite generic and we give examples of both topological defects (like vortices and monopoles) and topological textures (like Skyrmions) in 2 and 3 dimensions. The class of theories considered here is based on a kinetic term and three functionals often encountered in reduced Lagrangians for solitons. One particularly interesting case provides a generalization of the well-known Pohozaev identity. Our construction, however, is fundamentally different from scaling arguments behind Derrick's theorem and virial relations. For BPS vortices, we find interestingly an infinity of integrals simply related to the topological winding number.

AB - We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in d spatial dimensions. The construction provides five boundary charges that are related to certain integrals of the profile functions of the solitons in question. The framework is quite generic and we give examples of both topological defects (like vortices and monopoles) and topological textures (like Skyrmions) in 2 and 3 dimensions. The class of theories considered here is based on a kinetic term and three functionals often encountered in reduced Lagrangians for solitons. One particularly interesting case provides a generalization of the well-known Pohozaev identity. Our construction, however, is fundamentally different from scaling arguments behind Derrick's theorem and virial relations. For BPS vortices, we find interestingly an infinity of integrals simply related to the topological winding number.

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U2 - 10.1016/j.nuclphysb.2017.10.015

DO - 10.1016/j.nuclphysb.2017.10.015

M3 - Article

AN - SCOPUS:85034112688

SN - 0550-3213

VL - 925

SP - 500

EP - 535

JO - Nuclear Physics B

JF - Nuclear Physics B

ER -