Abstract
We study the half-BPS sector of the AdS/CFT correspondence. In the full sector of the correspondence, on-shell actions in the type IIB supergravity have been played crucial rolls. Therefore, we obtain an on-shell action corresponding to the LLM solution in the supergravity. The LLM solution is determined by a solution to a Dirichlet problem for a three-dimensional equation of motion. Our on-shell action is obtained by substituting this solution to the three-dimensional action. We explicitly verify that the on-shell action satisfies a Hamilton-Jacobi equation for the three dimensional action. We discuss what is dual to this on-shell action, in the system of N free fermions in a harmonic oscillator potential.
