| Abstract 摘要 | The way in which gauged supergravities can be embedded in higher-dimensional supergravities by means of dimensional reductions on spheres is highly non-trivial. We begin by reviewing some of the key ideas involved in Kaluza-Klein reductions, with a particular emphasis on the crucial issue of the consistency of the reduction. This is essential in order to ensure that the lower-dimensional theory is a true embedding, such that solutions in the lower-dimensional theory lift to solutions of the higher-dimensional theory. We will show in generic theories, dimensional reductions on spheres will not be consistent, and then we will show how particular supergravities evade such no-go theorems. We then turn to the specific case of the 7-sphere reduction of eleven-dimensional supergravity, which was shown by de Wit and Nicolai to give N=8 gauged SO(8) supergravity in four dimensions. We then report on our recent work, where the rather complicated expressions for the full N=8 reduction become considerably simpler in the truncation to N=2 gauged U(1)^4 STU supergravity. The embedding we obtain is sufficient for lifting most known solutions of four-dimensional gauged supergravity to eleven dimensions. |
