M-theory and the string genus expansion
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The partition function of the membrane is investigated. In particular, the case relevant to perturbative string theory of a membrane with topology $S^1 \times Σ$ is examined. The coupling between the string world sheet Euler character and the dilaton is shown to arise from a careful treatment of the membrane partition function measure. This demonstrates that the M-theory origin of the dilaton coupling to the string world sheet is quantum in nature.
12 pages, latex
12 pages, latex