Euclidean wormholes are exotic types of gravitational solutions that still challenge our physical intuition and understanding. After reviewing universal properties of asymptotically AdS wormhole solutions from a gravitational (bulk) point of view and the paradoxes they raise, I will describe some concrete (microscopic) field theoretic setups and models that exhibit such properties. These models can be reduced to matrix integrals and crucially involve correlated ("entangled") sums of representations of the boundary symmetry group. I will conclude with the realisation of such set-up in N=4 SYM/type IIB SUGRA.

Abstract: We are using holography to study quantum phase transitions in a 2+1 D strongly coupled non conformal gauge theory at finite chemical potential and magnetic field B. Our gravity dual is 4D N = 2 Fayet-Iliopoulos gauged supergravity. We found a line of quantum critical points at B= Bc between extremal dyonic black branes and extremal magnetically charged "thermal gas" solutions. We will introduce the two types of solutions, their thermodynamics and their phase diagram. Then we will discuss the physics of the critical point and we will point out qualitative similarities between our field theory and Nambu- Jona- Lasinio model in 2+1 D under the presence of an external magnetic field. We will conclude with some open questions both on the gravity and field theory side and we will discuss future directions.