Cutkosky Rules for Superstring Field Theory

TL;DR

This paper proves Cutkosky rules for superstring field theory, addressing the complex contour integrations needed due to exponential behavior of interaction vertices, and extends the results to general quantum field theories.

Contribution

It establishes Cutkosky rules for superstring field theory with complex contour integrations, also providing an alternative derivation for ordinary quantum field theories.

Findings

Proves Cutkosky rules for superstring field theory to all orders.

Addresses complex contour integration challenges in superstring amplitudes.

Extends the proof to a broad class of quantum field theories.

Abstract

Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.