I am learning stability conditions for derived categories of coherent sheaves, following Bridgeland, and coming from a vector bundles background. $\mu$-stability for vector bundles has a clear GIT origin (see Giesecker or the book of Mukai on invariants), hence I wonder if one could see the spaces of staibility conditions defined by Bridgeland as some sort of variation of GIT. Is it possible to draw such a connection?