Expansion of Lie algebras and accidental symmetries in Lovelock theories

Main properties of generalized contraction methods of Lie algebras, known also as expansion methods, are briefly introduced. Between some of their physical applications, one might study the nature of solutions in theories constructed with those expanded algebras. In particular, as we are interested in solutions that could be relevant in the context of AdS/CFT and Holographic Superconductors, we would like to study the holographic QFT dual to Chern-Simons gravity for an expansion of AdS algebra. As a first step, we studied charged static spherically symmetric BH solutions of a CS theory for the most simple extension of AdS symmetry: AdS×U(1). It is shown that in this kind of higher dimensional gravity, degeneracy in some sectors of the space of solutions can appear. In fact, arbitrary functions remain undetermined after the field equations are imposed. This is related to an increase in local symmetries and it is shown that the knowledge of these "accidental symmetries" can help to formulate a simple criterion that avoids unwanted degenerate ansatze. Finally, main properties of Pure Lovelock gravity are presented and some issues about black hole solutions this theory are also discussed.