How to tune into the quantum field?

AdS/CFT: Are Quantum Field Theory and String Theory really the same thing?

• I'm referring to the AdS/CFT correspondence. Which states that, for example, that there is a duality between String Theory in five dimensions and Quantum Field Theory in four dimensions. So String Theory is equivalent to Quantum Field Theory in one less dimension. I think that means if you want to get rid of String Theory, then you have to abandon all the principles of Quantum Field Theory? http://en.wikipedia.org/wiki/AdS/CFT_correspondence

• Answer:

  Both string theory and quantum field theory are actually mathematical frameworks upon which theories are built. String theory or quantum field theory, by themselves, are meaningless. You need to specify exactly which string theory and which quantum field theory you're talking about. If we take the case of quantum field theory for example, then the framework tells you how to deal with fields and perform calculations with them, but you still need to specify exactly what the fields are, what the interactions between them are, and so on. One such theory is the standard model of particle physics, which is a quantum field theory that describes how the strong, weak and electromagnetic fundamental forces work, what particles make up matter, and how they all interact. There are many other quantum field theories out there, but the standard model is so far the theory that best describes the universe we live in, and has been confirmed experimentally to very high precision. The AdS/CFT correspondence postulates that some specific types of string theories that are described in a particular geometry (anti-de Sitter, or AdS for short), are dual to some specific types of quantum field theories which belong to a particular category (conformal field theories, or CFT for short). What "dual" means in this context is, more or less, that certain parameters in the "bulk" (the AdS space) correspond to certain parameters on the "boundary" of that space (which is the CFT). It's certainly not true that any string theory must be dual to some quantum field theory (or vice versa). There are only a few pairs of theories for which the AdS/CFT correspondence actually works, and there are no known cases in which a string theory which is not in AdS space and/or a quantum field theory which is not a CFT are dual to each other. More generally, the holographic principle postulates (roughly) that for any quantum gravity theory (not limited to string theory; there are other theories out there), there should be some duality between a volume of space as described by the quantum gravity theory and the boundary of that volume as described by some theory without gravity (not necessarily a CFT). This postulate was motivated primarily by results from the semi-classical (that is, "semi-quantum") treatment of black holes, and in particular, the discovery that a black hole's entropy is proportional to its surface area rather than its volume. The AdS/CFT correspondence is the only concrete example of the holographic principle that we know of so far. Unfortunately, neither AdS nor CFT describe anything resembling the real world; nonetheless, AdS/CFT is an amazing result with countless theoretical applications. There is strong reason to believe that the holographic principle also applies in some way to the real world - the universe that we live in - but unfortunately, there is no proof so far. Thus, the discovery of a similar correspondence between a theory that does describe our universe and another theory would probably be the most incredible theoretical discovery in recent decades.