Multiloop $Φ^3$ Amplitudes from Bosonic String Theory

Details Multiloop $Φ^3$ Amplitudes from Bosonic String Theory Multiloop $Φ^3$ Amplitudes from Bosonic String Theory

1997-09-02

arxiv.org/abs/hep-th/9709019v1

Nucl.Phys. B515 (1998) 488-508

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1016/S0550-3213(97)00822-5

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 $\alpha' \to 0$ 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 $-4/\alpha'$.

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