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Various studies have attempted to extend the Witten's cubic open string fieldtheory to the cubic closed string field theory, which may describe Einsteingravity in the low energy sector consistently. In the present study we proposea cubic closed string field theory, introducing a double layer to describe theclosed string world-sheet as an extension of the open string world-sheet of theWitten's cubic open string. We mapped the closed string world-sheet onto thecomplex plane, of which the lower half plane is completely covered by theextended part of the string world-sheet. Using the Green's function on thecomplex plane, evaluated the Polyakov string path integral, from which weextracted the Neumann functions and the vertex operators. We obtained the oneand two string vertices (identities) following this procedure and finally thecubic string vertex operator. It is notable that the obtained cubic stringscattering amplitude coincide with the cubic graviton interaction of theEinstein gravity. Thus, the resultant cubic closed string field theoryconsistently describes the Einstein gravity. We also show that theKawai-Lewellen-Tye (KLT) relations of the first quantized string theory may bemanifested in the cubic closed string field theory.

Cubic Closed String Field Theory on a Double Layer