Ward Identities of W_{\infty} Symmetry and Higher Genus Amplitudes in 2D String Theory

Physics – High Energy Physics – High Energy Physics - Theory

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21 pages, Latex, 5 figures. Revised version published in Nucl. Phys. B. Errors of coefficients in some formula and the potenti

Scientific paper

10.1016/0550-3213(95)00607-9

The Ward identities of the $W_{\infty}$ symmetry in two dimensional string theory in the tachyon background are studied in the continuum approach. We consider amplitudes different from 2D string ones by the external leg factor and derive the recursion relations among them. The recursion relations have non-linear terms which give relations among the amplitudes defined on different genus. The solutions agree with the matrix model results even in higher genus. We also discuss differences of roles of the external leg factor between the $c_M = 1$ model and the $c_M <1$ model.

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