Abstract
The concept of the moduli space allows for a simple, universally applicable description of the low-energy dynamics of topological solitons. This description is remarkably insensitive to the properties of the underlying theory, whose details only manifest themselves via the moduli space metric. This article presents a generalization of this concept, which allows to transfer its most intriguing features to configurations of any energy captured by the theory giving rise to the soliton, given that these are localized sufficiently close to the soliton’s center. The resulting theory is capable of describing all dynamics within its range of applicability by just one family of fields, with all the information about the underlying theory entering via a finite number of background functions, which can be linked to physical properties of the present soliton.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G.S. Adkins, C.R. Nappi and E. Witten, Static Properties of Nucleons in the Skyrme Model, Nucl. Phys. B 228 (1983) 552 [INSPIRE].
J. Schechter and H. Weigel, The Skyrme model for baryons, hep-ph/9907554 [INSPIRE].
B. Moussallam, Casimir energy in the Skyrme model, Conf. Proc. C 9209271 (1992) 269 [hep-ph/9211229] [INSPIRE].
G.R. Dvali and M.A. Shifman, Dynamical compactification as a mechanism of spontaneous supersymmetry breaking, Nucl. Phys. B 504 (1997) 127 [hep-th/9611213] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [INSPIRE].
L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity, Phys. Rev. D 59 (1999) 086004 [hep-ph/9807344] [INSPIRE].
V.A. Rubakov and M.E. Shaposhnikov, Do We Live Inside a Domain Wall?, Phys. Lett. 125B (1983) 136 [INSPIRE].
J. Polchinski, TASI lectures on D-branes, in Fields, strings and duality. Proceedings, Summer School, Theoretical Advanced Study Institute in Elementary Particle Physics, TASI’96, Boulder, U.S.A., 2–28 June 1996, pp. 293–356 (1996) [hep-th/9611050] [INSPIRE].
M. Creutz, Quantum Mechanics of Extended Objects in Relativistic Field Theory, Phys. Rev. D 12 (1975) 3126 [INSPIRE].
J. Baacke and H.J. Rothe, Quantum States of Extended Objects Beyond the Coherent State Approximation, Nucl. Phys. B 118 (1977) 371 [INSPIRE].
J. Goldstone and R. Jackiw, Quantization of Nonlinear Waves, Phys. Rev. D 11 (1975) 1486 [INSPIRE].
L.D. Faddeev and V.E. Korepin, About the Zero Mode Problem in the Quantization of Solitons, Phys. Lett. 63B (1976) 435 [INSPIRE].
A. Jevicki, Treatment of Zero Frequency Modes in Perturbation Expansion About Classical Field Configurations, Nucl. Phys. B 117 (1976) 365 [INSPIRE].
R. Jackiw, Quantum Meaning of Classical Field Theory, Rev. Mod. Phys. 49 (1977) 681 [INSPIRE].
R. Rajaraman, Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory, North-Holland (1982) [INSPIRE].
M. Shifman, Advanced topics in Quantum Field Theory, Cambridge University Press (2012) [INSPIRE].
N. Manton and P. Sutcliffe, Topological Solitons, Cambridge Monographs on Mathematical Physics (2004) [INSPIRE].
J.-L. Gervais, A. Jevicki and B. Sakita, Perturbation Expansion Around Extended Particle States in Quantum Field Theory. 1, Phys. Rev. D 12 (1975) 1038 [INSPIRE].
J.-L. Gervais, A. Jevicki and B. Sakita, Collective Coordinate Method for Quantization of Extended Systems, Phys. Rept. 23 (1976) 281 [INSPIRE].
R.F. Dashen, B. Hasslacher and A. Neveu, Nonperturbative Methods and Extended Hadron Models in Field Theory 1. Semiclassical Functional Methods, Phys. Rev. D 10 (1974) 4114 [INSPIRE].
J. Goldstone, A. Salam and S. Weinberg, Broken Symmetries, Phys. Rev. 127 (1962) 965 [INSPIRE].
M. Srednicki, Quantum Field Theory, Cambridge University Press (2007) [INSPIRE].
M. Peskin and D. Schroeder, An Introduction To Quantum Field Theory, CRC Press (1995) [INSPIRE].
G.R. Dvali and M.A. Shifman, Tilting the brane, or some cosmological consequences of the brane universe, Phys. Rept. 320 (1999) 107 [hep-th/9904021] [INSPIRE].
S. Hofmann and M. Schneider, Classical versus quantum completeness, Phys. Rev. D 91 (2015) 125028 [arXiv:1504.05580] [INSPIRE].
G. Scharf, Finite Quantum Electrodynamics: The Causal Approach, Third Edition, Dover Books on Physics (2014).
S. Weinberg, Gravitation and Cosmology: Principles and applications of the general theory of relativity, Wiley (1972) [INSPIRE].
T.H.R. Skyrme, A Nonlinear field theory, Proc. Roy. Soc. Lond. A 260 (1961) 127 [INSPIRE].
H.B. Nielsen and P. Olesen, Vortex Line Models for Dual Strings, Nucl. Phys. B 61 (1973) 45 [INSPIRE].
A.J. Hanson, T. Regge, C. Teitelboim, Constrained Hamiltonian Systems, Academia Nazionale Dei Lincei (1976).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2001.09943
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Steingasser, T. On the domain of moduli fields. J. High Energ. Phys. 2020, 153 (2020). https://doi.org/10.1007/JHEP05(2020)153
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2020)153