A long time ago, physicists thought that only a small class of quantum field theories (QFT's) makes physical sense - those which are renormalizable. But then gradually it became accepted (Weinberg was the most influential figure in that regard) that QFT does not really need to be renormalizable, as long as it is viewed as an effective theory, not a fundamental one. Analogously, string theorists are used to think that only a small class of string theories make physical sense - those that live in the right number of dimensions (which unfortunately exceeds the observed number of dimensions). Even though they do not longer think that strings are fundamental (because they believe in existence of a more fundamental M-theory, which nobody really understands), they still seem to think that the number of dimensions is fixed. However, a recent paper http://lanl.arxiv.org/abs/1204.6263 argues that string theory, viewed as an effective theory, makes sense in any number of dimensions. I am not sure about the technical details, but conceptually it makes a lot of sense to me. What do you think?