FIELD CONFIGURATIONS AND THEIR INSTABILITY INDUCED BY HIGHER DIMENSIONS OF SPACE–TIME: AN EXAMPLE

Abstract

We use the model of L. Randall et al.3 to investigate the stability of allowed quantum field configurations. Firstly, we find that due to the topology of this five-dimensional model, there are two possible configurations of the scalar field, untwisted and twisted. They give rise to two types of instability. Secondly, when allowed to interact in the brane, the untwisted field 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 twisted field. On the other hand, the twisted field can make the two three-branes (that are otherwise identical in their properties and geometry) distinguishable therefore causing an energy difference between them. That is due to the antiperiodicity of the twisted fields, when rotating with π to go from one three-brane to the other. This energy difference between the branes renders 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 high dimension model, namely: higher dimensions, besides many other effects can also induce more than one field configuration and that can have consequences (e.g. instabilities) even after reducing the problem to four dimensions.