Unitarity of closed superstring perturbation theory

The box graph in superstring theory

“…Feynman's iǫ prescription on the particle propagators, together with Cutkowsky and Landau cutting rules guarantee a simple picture of the property of unitarity [6]. In string theory, unitarity of the amplitudes could be established only indirectly, by showing equivalence of the Lorentz covariant formulation with a manifestly unitary, but not manifestly Lorentz invariant formulation in the lightcone gauge [3]. For the convergence issue, no such indirect understanding is available at present.…”

“…In string theory, the equivalent of the iǫ prescription is understood only at a formal level through the connection with the light-cone gauge formulation [3,4]. Basically, the difficulty resides in the fact that it is not so natural to exhibit all intermediate string propagators in a dual diagram, though string field theory may well be able to produce such a representation [13].…”

“…Critical superstring theory automatically contains a massless graviton, as well as other particles, which interact consistently with general coordinate invariance. † The rules of superstring perturbation theory ensure causality, unitarity and Lorentz covariance [3,4], and there are strong indications that the scattering amplitudes are finite to all orders in perturbation theory [1,2,3,4,5].…”

Dispersion relations in string theory

“…Already substantial progress was made in obtaining a consistent formulation of perturbation theory as a sum over Riemann surfaces. In particular, it was shown that amplitudes defined this way are Lorentz invariant and perturbatively unitary [1], and it is generally believed that order by order, superstring loop amplitudes are finite. In particular, it was argued long ago that the Type II and heterotic amplitudes do not exhibit the tachyon and massless dilaton tadpole divergences that are known to occur in the bosonic string [2][3] [4].…”

Momentum analyticity and finiteness of the 1-loop superstring amplitude

“…Another way to say this is that unlike in quantum field theory, one has not properly provided an iǫ prescription for the string propagators [5]. This issue was addressed in the field theory limit of superstring theory in [6,7].…”