Deriving Gauge-String Duality

Gauge (or Yang-Mills) theories are the building blocks of our current physical understanding of the universe. In parallel, string theory is a framework for a consistent quantum description of gravity. Gauge-String duality a.k.a. the AdS/CFT correspondence proposes a remarkable connection between these two very different classes of theories. I will begin by discussing why it is important to arrive at a first principles understanding of the underlying mechanism of this duality relating quantum field theories and string theories (or other theories of gravity). I will then proceed to discuss a very general approach which aims to relate large N QFTs and string theories, starting from free field theories. This corresponds to a tensionless limit of the dual string theory on AdS spacetime. Finally, I will discuss specific cases of this limit for 3d AdS (dual to 2d CFT) and 5d AdS (dual to 4d Super Yang-Mills theory), where one has begun to carry this program through to fruition, going from the string theory to the field theory and vice versa.