Low energy physics for the high energy physicist - Effective theories, holographic duality and all that

In this work we discuss the application of high energy theory methods to the study of condensed matter problems. We focus in particular on the effective field theory (EFT) approach and on the holographic duality. We show that, in certain contexts, both techniques present some relevant advantages with respect to more standard approaches. In particular, we will study holographic superfluids, and make explicit connection between the holographic picture and the EFT one. We also determine for the first time the gravity dual of a solid, and show that it undergoes a first order phase transition, a “holographic melting”. On a more phenomenological ground, we study the motion of vortex lines in a confined superfluid. Using a suitable EFT we successfully reproduce the experimental results, and perform a number of steps forward with respect to traditional methods. Finally, we also discuss possible exciting directions for the future of EFTs and condensed matter.