Higher-derivative theories of gravity in anti-de Sitter space can be used as holographic toy models that capture a broader universality class of CFTs than those covered by holographic Einstein gravity. In this talk, I will consider higher-derivative theories of gravity and electromagnetism and I will use them to explore aspects of holographic CFTs at a finite chemical potential. The theories I employ are of a new type that allow one to perform many exact and analytic computations. I will compute several entries in the holographic dictionary of these theories, some of which are trivial for Einstein-Maxwell theory. The parameters of the theories are constrained by imposing bulk causality and boundary unitarity and I will also discuss positive-entropy bounds related to the weak gravity conjecture. Then I will discuss several properties of the hypothetical dual CFTs at finite chemical potential, such as thermodynamic phase space, hydrodynamics and entanglement structure, focusing on the differences with respect to Einstein-Maxwell. I will use these results to show that these holographic theories satisfy a number of universal relations involving twist operators (which are known to hold for arbitrary CFTs), and to establish a novel universal formula for the charged entanglement entropy across a spherical region.
DFA & INFN
