Abstract
We use results of Verlinde and Verlinde [Phys. Lett. B 192 (1987) 95] to evaluate explicitly the two-loop partition function for ten-dimensional closed superstrings in a BRST-invariant manner. By taking picture-changing operators to a ramification point on the surface and using the Riemann identity we obtain a simple expression in terms of theta functions which is known to vanish.
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