I have read Joseph Polchinski’s excellent review paper titled “Dualities of Fields and Strings“. This paper is written for experts. I am not an expert in fields and strings. I am not an expert in dualities either but I was able to understand the gist of his arguments. I recommend this paper highly to every serious student of physics.
For me the most interesting paragraphs were the following:
“The original wave-particle duality already exemplified this idea: given a QFT, one can take two different classical limits depending on what one holds fixed. One limit gives classical fields, the other classical particles. It is fruitless to argue whether the fundamental entities are particles or fields.”
“A notable conclusion is that there is only a single quantum theory in the end: what appear to be different string theories are different classical limits of a single quantum theory, whose full form is not yet known.”
“After the early successes of string theory, a tempting direction was to seek a nonperturbative formulation of the theory in terms of the quantum mechanics of strings. But work in this direction, such as abstract conformal field theory, and string field theory, seem not to have been so fruitful. Rather, strings have been a bridge to the discovery of M theory, in which they are found to emerge in some classical limits but not in others.”
“The existence of dualities points to a great unity in the structure of theoretical physics. String-string dualities imply that there is a unique string/M theory. Unique here means that there are not even adjustable coupling constants, as in quantum field theory; rather, the apparent parameters are properties of the particular state (vacuum) of the system. Gauge/gravity dualities further imply that many QFT’s can also be interpreted as vacua of string theory. As we have noted, a necessary condition for a QFT to have an interpretation in terms of a geometrical spacetime is that the number of fields be large. However, there is no sharp cutoff on the number of fields, so QFT’s with small numbers of fields should correspond to string theories in highly curved spaces. In this sense it may be that every QFT can be understood as a vacuum state of string/M theory.”
“When we identify the different duality frames with different fundamental descriptions, we are essentially saying that what is fundamental is what we see in the classical limit. This is strange, in a world that is intrinsically quantum mechanical (and what of theories that have no classical limit?). But our universal tool for constructing relativistic quantum field theories, the path integral, begins with a sum over classical histories. Somehow we do not have a fully quantum point of view, and this may be connected with our inability to derive the interesting dualities.”