Catoptric tadpoles

Fermionic string perturbation theory is known to suffer from an ambiguity in the form of a total derivative in the moduli space. For a class of backgrounds (including R¹⁰, orbifolds and theories with no U(1) factors in gauge group) we show that these ambiguities for the partition function of heterotic string theory at any genus are proportional to massless physical tadpoles in the theory at lower genera and hence vanish in stable vacua. We also find that in R¹⁰ the cosmological constant at a given genus is proportional to the cosmological constant at lower genera. This enables us to give an inductive argument for the vanishing of the cosmological constant in R¹⁰ to all orders in string perturbation theory. We also address the ambiguity and finiteness of n-point functions. Our results indicate that in R¹⁰ the ambiguity can be absorbed by a renormalization of the string coupling constant and the string tension. The expected sources of divergence in the n-point function in arbitrary tachyon-free backgrounds, besides the usual infrared divergences for d ≤ 4, are shown to be proportional to tadpoles of physical massless fields. For type II strings in arbitrary backgrounds, we show by explicit calculations that the ambiguity vanishes at g = 2.