Holography and Integrability in String Theory

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Our understanding of the force that binds together the fundamental constituents (quarks and gluons) of atomic nuclei is based on a theory called quantum chromodynamics. At very high energies the quarks move freely and we have a good description of what is going on. On the other hand, at everyday energies the quarks are confined together and our current theoretical tools and computational skills are very far from providing a good physical picture of the system. In technical terms, we have asymptotic freedom at short distances and confinement at large distances. The most basic questions such as what is the mass of a proton can not be accessed with our current theoretical tools. To understand nature at these scales we must develop new mathematical tools and better physical intuition. For some particle theories, the tools we were looking for seem to be at hand and go by the name of Holography and Integrability (i.e. exact solvability). These field theories also describe, in an holographic sense, the dynamics of a quantum theory of gravity called string theory. With the help of Integrability and Holography techniques we are thus moving closer to merging Einstein's theory of gravity and quantum mechanics, one of the most beautiful and important open problems in physics.