EFFECTIVE FIELD THEORIES
As we have seen repeatedly, a description of fundamental particles in terms of quantum field theory is beset by infinities and divergences. Most of these result from the fact that physically, fundamental particles such as leptons, quarks and field bosons, are apparently literally pointlike. One elegant solution to these difficulties is an effective field theory.

That is, instead of dealing with bare vertices which as you zoom in on them exhibit more and more complex virtual processes at smaller and smaller scales, cover the vertex with a blob and stop at the surface of the blob. The most successful early example of such an approach was Fermi's 1930 theory of β decay, in which the actual weak vertex, which would have had to involve one or more bosons, was replaced by a three-vertex: n → p + e− + bar-νe.

This kind of approach is extremely useful in phenomenology of fundamental processes.




GRAND UNIFIED THEORIES


At around 1015 to 1016 GeV, the running coupling constants for strong, weak and electromagnetic processes tend to approach one another closely, so in the mid-1970s a variety of physicists started working on the unification of all gauge field theories.  Since then, around a dozen different approaches have been suggested, none of which have made predictions that are currently confirmable by experiment.  Almost all these GUT approaches use some version of Supersymmetry.  Also, almost all later attempts to get beyond the Standard Model, including String Theory, contain some aspects of the earlier GUT approaches. Just about any version of a GUT theory predicts proton decay, and also predicts the existence of many exotic particles and structures, often characteristic of the specific theory, for which no evidence has been found.



One mathematically elegant way to avoid the usual singularities of field theory is to replace point particles by objects with a finite size, usually taken to be around 10−33 cm (in other words, at the Planck scale). All string theories include both closed and open strings.  Different particles correspond to different quantum modes of the string, and fissioning and fusing of strings produce particle emission and absorption.  Similarly, initially open strings can convert into closed strings.  One of the big attractions string theories have always had for theorists is that they naturally include a spin-2 boson, which can be obviously identified with the graviton, thus suggesting that string theories are also quantum theories of gravity.  Progress was held up for a while because five different versions of string theory were known. Modern string theory began about 1970, but was beset by severe mathematical difficulties which were not resolved until 1984. Since then string theory has reigned supreme. In the early 1990s, it was found that a single unified framework could contain all known versions of string theory as limiting cases. The general framework is usually called M-Theory.


Edward Witten (1951 - )

One of the facts about string theories before the mid 1990s that caused widespread dismay in physics is that all the existing versions of the theory required 10 dimensions of space-time. Six of these were necessarily “compact,” curled up to a Planck-scale length, to produce the universe of four extended dimensions in which we obviously live. The generalization, M-theory, requires 11 dimensions, but actually the number of space-time dimensions in such approaches is not really fixed. It is notorious that string theory and its generalization, M-theory, have never made contact with any aspect of reality, and this has generated many criticisms from respected physicists. However, as in the case of cosmic inflation, the criticisms have not been accompanied by viable alternative approaches, and in the search for a general theory of all particles and forces, string theory/M-theory still looks like the only game in town.






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