Multiloop ${\Phi }^3$ Amplitudes from Bosonic String Theory

Abstract

We show how the multiloop amplitudes of ${\Phi }^3$ theory (in the worldline formulation of Schmidt and Schubert) are recovered from the N-tachyon $(h+1)$-loop amplitude in bosonic string theory in the ${\alpha }^{\prime }\to 0$ limit, if one keeps the tachyon coupling constant fixed. In this limit the integral over string moduli space receives contributions only from those corners where the world-sheet resembles a ${\Phi }^3$ particle diagram. Technical issues involved are a proper choice of local world-sheet coordinates, needed to take the string amplitudes off-shell, and a formal procedure for introducing a free mass parameter $M^2$ instead of the tachyonic value $-4/{\alpha }^{\prime }$.

1+26 pages (Latex), 4 figures included (PicTex)

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