Topological Amplitudes in String Theory

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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31 pages (LATEX) + 2 figures (available upon request as PS file or hardcopy), NUB-3071 - IC/93/202 - CPTH-A258.0793

Scientific paper

10.1016/0550-3213(94)90617-3

We show that certain type II string amplitudes at genus $g$ are given by the topological partition function $F_g$ discussed recently by Bershadsky, Cecotti, Ooguri and Vafa. These amplitudes give rise to a term in the four-dimensional effective action of the form $\sum_g F_g W^{2g}$, where $W$ is the chiral superfield of $N=2$ supergravitational multiplet. The holomorphic anomaly of $F_g$ is related to non-localities of the effective action due to the propagation of massless states. This result generalizes the holomorphic anomaly of the one loop case which is known to lead to non-harmonic gravitational couplings.

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