We have studied the existence of topological Bogomol'nyi-Prasad-Sommerfield or self-dual configurations in a Lorentz-violating gauged O(3) nonlinear sigma model, where CP T -even Lorentzviolating (LV) terms were introduced in both the gauge and σ-field sectors. As happens in the usual gauged σ model, purely magnetic self-dual configurations are allowed, maintaining some qualitative features of the standard ones. In a more involved configuration, Lorentz violation provides new self-dual magnetic solutions carrying an electric field but a null total electric charge. In both cases, the total energy of the self-dual configurations turns out to be proportional to the topological charge of the model and to the LV parameters introduced in the σ sector. It is shown that the LV terms yield magnetic flux reversion as well.

Within the superfield approach, we formulate the superfield supersymmetric aether-like Lorentzbreaking models, both in three-and in four-dimensional cases.

We study the one-loop effective potential for some Horava-Lifshitz-like theories.The Horava-Lifshitz (HL) approach [1] has recently acquired a great scientific attention. This approach is characterized by an essential asymmetry between space and time coordinates (space-time anisotropy): the equations of motion of the theory are invariant under the rescaling x i → bx i , t → b z t, where z, the critical exponent, is a number characterizing its ultraviolet behaviour. The main reason for it is that for the HL-like reformulation of the known field theory models with a nontrivial critical exponent z > 1 leads to an improvement of the renormalization of these models. In particular, the four-dimensional gravity becomes renormalizable at z = 3.Different issues related to the HL gravity, including its cosmological aspects [2], exact solutions [3], black holes [4] were considered in a number of papers. At the same time, the study of the impacts of the HL extension to other field theories is a very interesting problem. Some aspects of the HL generalizations for the gauge field theories were presented in [5]. Renormalizability of the scalar field theory models with space-time anisotropy has been discussed in details in [6]. The four-fermion HL-like theory has been studied in [7].The Casimir effect for the HL-like scalar field theory has been considered in [8]. In [9], the HL modifications of the CP N −1 were studied. The possibility of restoration of the Lorentz symmetry in the theories with the space-time anisotropy is discussed in [5,10].It is well known that the effective potential is a key object in the quantum field theory useful for studying many of its aspects. Some interesting results for the HL-like theories have been obtained in the papers [11,12] where the effective potential for the φ 4 and the Liouville- * Electronic address: cffarias,jroberto,petrov@fisica.ufpb.br † Electronic address: mgomes,ajsilva@fma.if.usp.br 2 Lifshitz theories have been studied. Also, some interesting results for the effective potential in scalar field theories with certain values of the critical exponent, have been obtained in [13]. In this paper, we intend to study the effective potential for a more generic class of theories including an arbitrary interaction of the scalar field with other fields. In the sequel, we will treat three cases, namely, a pure scalar model, a gauge model and a Yukawa model. a. Scalar model. We start with the straightforward HL generalization of the usual scalar model:The renormalizability of such a model has been discussed in [6]. In general, renormalizability of such models requires a polynomial form of the potential, however, for simplicity we restrict ourselves to the form V (φ) = λφ n . Here our aim is the study of its effective potential. To proceed with it, we, as usual, make the replacement φ → Φ + φ, where Φ is a background field, and φ is a quantum one. For the one-loop calculations, it is sufficient to keep only the terms of the second order in the quantum field φ:Following the standard procedure, ...

We have shown the existence of self-dual solitons in a type of generalized Chern-Simons baby Skyrme model where the generalized function (depending only in the Skyrme field) is coupled to the sigma-model term. The consistent implementation of the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism requires the generalizing function becomes the superpotential defining properly the selfdual potential. Thus, we have obtained a topological energy lower-bound (Bogomol'nyi bound) and the self-dual equations satisfied by the fields saturating such a bound. The Bogomol'nyi bound being proportional to the topological charge of the Skyrme field is quantized whereas the total magnetic flux is not. Such as expected in a Chern-Simons model the total magnetic flux and the total electrical charge are proportional to each other. Thus, by considering the superpotential a wellbehaved function in the whole target space we have shown the existence of three types of self-dual solutions: compacton solitons, soliton solutions whose tail decays following an exponential-law e −αr 2 (α > 0), and solitons having a power-law decay r −β (β > 0). The profiles of the two last solitons can exhibit a compactonlike behavior. The self-dual equations have been solved numerically and we have depicted the soliton profiles, commenting on the main characteristics exhibited by them.

We calculate the one-loop effective potential for Horava-Lifshitz-like QED and Yukawa-like theory for arbitrary values of the critical exponent and the space-time dimension.a. Introduction. The Horava-Lifshitz (HL) methodology based on the essential asymmetry between time and space coordinates [1] has been originally introduced within the context of the search for the perturbatively consistent gravity theory. The main advantage of this concept consists in the fact that, from one side, it improves the renormalizability of the field theory models, and, from another side, it avoids arising of the ghosts whose presence is characteristic for the theories with higher time derivatives [2]. Therefore this concept (or, more generally, the concept of the time-space asymmetry) began to be applied not only within studies of gravity but also for the consideration of other (f.e. scalar and vector) field theory models.One line of studies of the theories with the time-space asymmetry is devoted to investigation of their renormalizability and renormalization. Within this context, the HL versions of the gauge field theories [3], scalar field theories [4] (see also [5] for the renormalization group issues), four-fermion theory [6] and CP N −1 model [7] were considered. Another important result in this context is the generalization of the Ward identities for the HL-like theories [8].Another line of the studies of the HL-like theories is devoted to the effective potential in such theories. In the papers [9-12] the one-loop effective potential for the scalar field theories with different forms of self-coupling and arbitrary values of z, for the scalar QED with z = 2 and z = 3, and for the Yukawa model with z = 2 and z = 3 has been obtained.However, the interesting problem is the calculation of the (one-loop) effective potential in the scalar QED and Yukawa model with an arbitrary value of the critical exponent. This