  We study the five-dimensional supergravity dual of the a-maximization under
AdS5/CFT4 duality. We firstly show that the a-maximization is mapped to the
attractor equation in five-dimensional gauged supergravity, and that the trial
a-function is the inverse cube of the superpotential of the five-dimensional
theory.
  There is also a version of a-maximization in which one extremizes over
Lagrange multipliers enforcing the anomaly-free condition of the R-symmetry. We
identify the supergravity dual of this procedure, and show how the Lagrange
multipliers appearing in the supergravity description naturally correspond to
the gauge coupling of the superconformal field theory.
