A truncation of string field theory is compared with the duality invariant effective action of D = 4, N = 4 heterotic strings to cubic order. The three-string vertex must satisfy a set of compatibility conditions. Any cyclic three-string vertex is compatible with the D = 4, N = 4 effective field theory. The effective actions may be useful in understanding the non-polynomial structure and the underlying symmetry of covariant closed string field theory, and in addressing issues of background independence. We also discuss the effective action and string field theory of the N = 2 string.
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I would like to thank 0. Lechtenfeld, A. Shapere, and E. Witten for discussions, and especially B. Zwiebach for a lot of help and for a critical reading of the manuscript. This work is supported in part by DOE grant DE-FGO2-90ER40542.