Four Dimensional Supergravity from String Theory

A derivation of N=1 supergravity action from string theory is presented. Starting from a Nambu-Goto bosonic string, matter field is introduced to obtain a superstring in four dimension. The excitation quanta of this string contain graviton and the gravitino. Using the principle of equivalence, the action in curved space time are found and the sum of them is the Deser-Zumino N=1 supergravity action. The energy tensor is Lorentz invariant due to supersymmetry.Comment: 9 page