Abstract
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.
Highlights
Readjustments and probably are a reflection of general deep problems [8]
In this spirit we present here exact solutions and BPS stability discussions of specific Lifshitz field theories (BPS solitons in Lifshitz theories have been found in [11]), related naturally to special solvable topological soliton models without quadratic terms [12]–[22], with special diffeomorphism (SDiff) invariance, which, as we will show, contain in a way some of the anisotropic scaling features, like symmetries
We further show that these Lifshitz soliton models contain submodels with invariance under the infinite-dimensional group of area or volume preserving diffeomorphisms (SDiff symmetry, in general)
Summary
It is well-known that the presence of higher derivatives in the terms of a field theory lagrangian which contribute to the propagator (i.e., terms quadratic in the fields and their derivatives) improves the UV behaviour of the theory, because the propagator in momentum space will contain higher powers of momenta in the denominator. We want to consider terms which are related to topological charge or winding number densities, which in d space dimensions have the typical form. It is interesting to compare the symmetries of the actions (2.5) with the symmetries of the BPS-Skyrme type theories [12]–[22] whose actions are the Lorentz-invariant generalizations to time-dependent field configurations of the above energy (2.6), i.e., their actions have the form. While the actions (2.5) still have the base space SDiffs as symmetries (these are, Noether symmetries), but no longer the target space SDiffs (more precisely, the subgroup which leaves the potential invariant), the situation is exactly the other way round for the theories (2.7). For reasons of simplicity we restrict our examples to baby skyrmions
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