Abstract
A class of effective field theories for moduli or collective coordinates on solitons of generic shapes is constructed. As an illustration, we consider effective field theories living on solitons in the O(4) non-linear sigma model with higher-derivative terms.
Highlights
Effective field theory is one of the most useful tools available to date
Higher-order corrections coming from the lower-order terms, as mentioned above, can be calculated systematically [7], but we will not consider them in this Letter; i.e., here we present only the leading-order effective action
We have developed a basic framework for calculating effective actions on, in principle, generic solitons
Summary
Effective field theory is one of the most useful tools available to date. Even the standard model, renormalizable in its present formulation, may be just an effective theory of Nature where possible supersymmetric and/or grand unified extensions have been integrated out. Effective field theories for moduli have been constructed for many kinds of solitons, but very often only in cases where the soliton has a simple, flat or straight shape. When solitons are particle-like such as monopoles this can describe the low-energy dynamics of the solitons in a compact way as geodesics of moduli spaces [1], while for solitons being extended objects such as domain walls or vortices, this describes field theories on their world-volume, as in the case of D-branes in string theory or more general branes. In this Letter we construct a first attempt of effective field theories in principle applicable to solitons of generic shapes and apply it to a class of models possessing soliton solutions of flat, spherical, cylindrical and toroidal shapes
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