Field configurations and their instability induced by higher dimensions ofspace-time: An example

We use the model of L. Randall et al.(3) to investigate the stability of al lowed quantum field configurations. Firstly, we find that due to the topolo gy of this five-dimensional model, there are two possible configurations of the scalar field, untwisted and twisted. They give rise to two types of in stability. Secondly, when allowed to interact in the brane, the untwisted f ield is shown to be unstable even if it is at the true vacuum ground state as a result of one-loop corrections that arise from coupling with the twist ed field. On the other hand, the twisted field can make the two three-brane s (that are otherwise identical in their properties and geometry) distingui shable therefore causing an energy difference between them. That is due to the antiperiodicity of the twisted fields, when rotating with pi to go from one three-brane to the other. This energy difference between the branes re nders the fifth dimension unstable. This toy model is simple enough to use to illustrate a point that can be important for the general case of any hig h dimension model, namely: higher dimensions, besides many other effects ca n also induce more than one field configuration and that can have consequen ces (e.g. instabilities) even after reducing the problem to four dimensions .