Quantization and Scattering in the IIB SL(2,Z) Covariant Superstring

TL;DR

This paper reformulates the IIB superstring action in a covariant SL(2,Z) framework, deriving sector-specific amplitudes and comparing them to previous conjectures, revealing new insights into string scattering.

Contribution

It presents a new Polyakov form of the SL(2,Z) covariant IIB superstring action and computes sector-specific graviton scattering amplitudes.

Findings

SL(2,Z) invariant amplitudes derived from summing over sectors

Tree-level four-graviton amplitude differs from previous conjectures

Both formalisms agree at order ^3 in '

Abstract

We rewrite the SL(2,Z) covariant worldsheet action for the IIB string proposed by Townsend in a Polyakov form. In a flat background the formalism yields separate (p,q) sectors. In each one the action is that of the IIB string action with the string slope parameter \alp\pr replaced by its SL(2,Z) analogue \alp_{pq}\pr. SL(2,Z) invariant graviton scattering amplitudes are obtained from those of the fundamental (1,0) string by summing over the different sectors. The tree-level four-graviton amplitude in this formalism differs from a previously conjectured non-perturbative form; both yield the same expansion in order \alpha\pr^3.