An Ambiguity in Fermionic String Perturbation Theory*

Recent investigation by Verlinde and Verlinde has shown that the fermionic string loop amplitudes change by a total derivative term in the moduli space under a change of basis of the supermoduli. This ambiguity is addressed in the context of the heterotic string theory, and shown to be a consequence of an inherent ambiguity in defining integration over the variables of a Grassmann algebra-in this case the Grassmann valued coordinates of the supermoduli space. A resolution of this ambiguity in genus-two within this formalism is also presented. Submitted to Nuclear Physics B * Work supported in part by the Department of Energy, contracts DE-AC02-76ER02220 (Princeton), DE-AC02-82ER40073 (UCSD), and DE-AC03-76SF00515 (SLAC). + Address after March 1, 1988: Theoretical Physics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India.