Quantum field theory at finite coupling through the holographic string

<!--HTML-->Abstract - Gauge theories lie at the heart of our understanding of the elementary particles in nature. Moreover, through the gauge-gravity duality they also provide us with a non-perturbative description of quantum gravity. Yet, we lack of the mathematical tools to describe phenomena at generic strength of the interaction. In this talk we will survey some of the exciting recent developments in exploring gauge theories and their dual description in terms of strings at finite coupling. The main objective of our study will be a most symmetric gauge theory known as N=4 super Yang-Mills theory. That theory is expected to play an analogues role in Quantum Field Theory to the one played by the Hydrogen atom in Chemistry. We will review new techniques that are motivated by the dual string description and are based on Integrability and Holography. These techniques allow for the first time exact computation of dynamical quantities at any strength of the interaction. We will focus on the computation of scattering amplitudes and will present a new result for the full six gluon amplitude at finite coupling.