  In four dimensional N=1 supersymmetric field theory it is often the case that
the $U(1)_R$ current that becomes part of the superconformal algebra at the
infrared fixed point is conserved throughout the renormalization group (RG)
flow. We show that when that happens, the central charge $a$ decreases under RG
flow. The main tool we employ is an extension of recent ideas on
``$a$-maximization'' away from fixed points of the RG. This extension is useful
more generally in studying RG flows in supersymmetric theories.

High Energy Physics - Theory