Gravitating multidefects from higher dimensions
نویسنده
چکیده
Warped configurations admitting pairs of gravitating defects are analyzed. After devising a general method for the construction of multidefects, specific examples are presented in the case of higher-dimensional Einstein-Hilbert gravity. The obtained profiles describe diverse physical situations such as (topological) kink-antikink systems, pairs of non-topological solitons and bound configurations of a kink and of a non-topological soliton. In all the mentioned cases the geometry is always well behaved (all relevant curvature invariants are regular) and tends to five-dimensional anti-de Sitter space-time for large asymptotic values of the bulk coordinate. Particular classes of solutions can be generalized to the framework where the gravity part of the action includes, as a correction, the Euler-Gauss-Bonnet combination. After scrutinizing the structure of the zero modes, the obtained results are compared with conventional gravitating configurations containing a single topological defect. Electronic address: [email protected] 1 Formulation of the problem Solitons represent an important class of phenomena both in classical and quantum field theory. Solitonic solutions include monopoles, skyrmions, vortices an kinks [1]. It is well known that in (1 + 1) dimensional field theories (static) topological solitons can arise in combination with an appropriately non-linear interaction potential [2, 3]. These solutions are customarily called kinks and they may arise either in the case of polynomial potential or in the case of sine-Gordon potentials [1, 4, 5]. In (1+ 1) dimensions, spatial infinity consists of two points (i.e. ±∞) and the kink solution typically interpolates between two minima of the underlying potential. The topological charge of the kink is positive. If the kink solution exist, there will also typically exist the related antikink solution whose topological charge will be opposite to the one of the kink. In recent years general methods have been devised for the analysis of the complicated nonlinear problem arising in the case of (1 + 1)-dimensional multidefect systems [6, 7, 8, 9, 10]. It is also well known that, in (1+1), dimensions non-topological solitons can occur. These objects have vanishing topological charge since the field profile vanishes for large absolute value of the spatial coordinate [11]. It is finally known that, with the appropriate field content, multidefects do arise in (1+1) dimensions [2, 3, 8, 10]. These solutions include, for instance bound states of a kink and of an antikink and the so-called trapping bag solutions [3, 12] where a non-topological profile is supplemented by a kink (or an antikink) profile. There are mathematical and physical analogies between the defects of (1+1) dimensional field theories and the gravitating solitonic solutions of five-dimensional gravity. In the latter case the rôle of the spatial coordinate is played by the fifth dimension parametrizing the field profile in the bulk space-time. Along this perspective it is known that gravitating kink solutions may arise, for instance, in the context of five-dimensional Einstein-Hilbert gravity. Different groups analyzed single kink solutions in higher-dimensional geometries. In particular examples are known both in flat five-dimensional space-time [13] (see also [14]), and in five-dimensional (warped) space-times [15, 16, 17, 18, 19, 20] (see also [22, 23] for an interesting perspective). While the compatibility of these configurations with higher-dimensional Einstein-Hilbert gravity has been ascertained, interesting generalizations contemplate the coupling of the scalar degree of freedom to the curvature [24, 25, 26], the inclusion of GaussBonnet self-interactions [27, 28, 29, 30, 31], the addition of more than one internal (warped) dimension (see, for instance, [32, 33, 34]). While the features of the geometry may be diverse, it is certainly plausible (even if not mandatory) that gravitating kink solutions lead to five-dimensional anti-de Sitter geometry ( AdS5 in the following) for large absolute values of the bulk coordinate. In a related framework it is also possible to obtain kink profiles whose related geometry leads, for large absolute values of the bulk radius, to five-dimensional Minkowski space-time. Moreover, single defects with non-topological features have been studied in [35]. It should be stressed that gravity is an essential ingredient for all the five-
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تاریخ انتشار 2006