String Theory

The incompatibility between local quantum field theory, which is the theoretical framework which very successfully describes elementary particle physics, i.e. physics at very small scales, and general relativity, which is the basis of cosmology, i.e. physics at very large scales, is one of the main open problems in theoretical physics. String theory is an attempt at its resolution. While it was originally formulated as a theory of the strong interactions, it was soon realized that the theory always contains a massless spin two excitation which can be interpreted as the graviton, the quantum of the gravitational interaction. But the graviton is not the only excitation of the string. There is an infinite number of them and the massless ones, besides the graviton, can be interpreted e.g. as non-abelian gauge bosons and massless matter fermions. In this way string theory enforces the unification of all elementary particles and all their interactions. Since it is formulated as a quantum theory, it achieves the unification of general relativity with quantum theory, albeit not within the framework of local quantum field theory. The latter emerges as an effective low energy description of the massless excitation modes of the string.

While, to the best of our knowledge, being a consistent theory, the crucial question is whether Nature has chosen this possibility of reconciling quantum theory with gravity. String theory makes many postdictions, such as the existence of gravity, but it makes also many predictions, e.g. an infinite tower of massive excitations or corrections to Einstein’s theory of gravity. Unfortunately, to test these predictions requires energies which are unobtainable in experiments by many orders of magnitude. The characteristic energy scale is the Planck scale which is intrinsic to the gravitational interaction and every alternative theory of quantum gravity will have to face the same problem regarding its verifiability.

While string theory might be the dream of a final theory come true, it can also be viewed, similar to quantum field theory, as a framework in which many physical questions can be formulated and answered. This is known as the AdS/CFT correspondence, of more generally the gauge/gravity duality or even more generally, the holographic principle. It states, very roughly, that a field theory without gravity in d dimensional space-time has an alternative (dual) description as a string theory in d+1 dimensions. The difference in dimensions makes this duality holographic. This can be made very explicit in certain examples and is being applied in many areas of theoretical physics and even information theory.

When assessing string theory it should be kept in mind that it has led to a number of interesting developments in physics and mathematics. As such it played a prominent role in theoretical and mathematical physics of the past 50 years and is expected to do so in the future. Even if its role as a quantum theory of gravity cannot be conclusively, i.e. experimentally, verified, it has greatly enlarged the horizon within which we formulate and study physical systems.