How to Construct a Holographic EFT for Phonons
2020 April 07
These notes are based on a series of lectures given at the XV Modave Summer School in September, 2019. The course was organized in five lectures on Holographic techniques applied to condensed matter physics. In order to be self consistent, in the first three lectures I introduced the basic concepts of the so called holographic dictionary. Since AdS/CFT is by now a very well established framework to analyze strongly coupled quantum field theories, and many good reviews have been written on the topic I decided to refer to the existing literature for the basic derivation of the holographic dictionary. What illustrated in here consists instead in the analysis of a holographic model which breaks translation spontaneously or pseudo-spontaneously, the holographic realization of a charge density wave. Part of the computations outlined in this manuscript, and in particular the derivation of the Ward Identities, have never appeared in the literature so far. The paper constitute a small exercise which a reader interested in learning more advanced techniques to analyze bottom-up holographic models can use as a warm up to eventually tackle more difficult tasks.