Exact Results in Quantum Theory & Gravity

AdS/CFT correspondence is conjecture about connections between conformal field theory in d dimensions and gravity with negative cosmological constant in (d+1) dimensions. Despite its huge popularity, it is not yet well understood because any test demands great deal of complicated calculations. As a result, people are tend to work on some low-dimensional toy models. I will discuss one of them – SYK model, theory which is supposed to be dual to 2-dimensional black hole spacetime. After that, we will focus on another (slightly non-equivalent) formulation of SYK model as Gurau—Witen theory which seems to be more natural one. Last but not least, we shall discuss recent generalization conjectured by Klebanov and proven in [1].Talk partially based on:[1] arXiv:1712.00249