Chiral strings, the sectorized description and their integrated vertex operators

TL;DR

This paper develops a method to define integrated vertex operators for chiral strings, enabling the calculation of higher-point scattering amplitudes and connecting to known results in the tensionless limit.

Contribution

It introduces a sectorized interpretation to define integrated vertex operators for chiral strings, facilitating higher-point amplitude computations.

Findings

Integrated vertex operators for chiral strings are successfully constructed.

Higher-point amplitudes match known results in the tensionless limit.

The sectorized approach emulates left/right factorization in scattering amplitudes.

Abstract

A chiral string can be seen as an ordinary string in a singular gauge for the worldsheet metric and has the ambitwistor string as its tensionless limit. As proposed by Siegel, there is a one-parameter ($\beta$) gauge family interpolating between the chiral limit and the usual conformal gauge in string theory. This idea was used to compute scattering amplitudes of tensile chiral strings, which are given by standard string amplitudes with modified ($\beta$-dependent) antiholomorphic propagators. Due to the absence of a sensible definition of the integrated vertex operator, there is still no ordinary prescription for higher than $3$-point amplitude computations directly from the chiral model. The exception is the tensionless limit. In this work this gap will be filled. Starting with a chiral string action, the integrated vertex operator is defined, relying on the so-called sectorized interpretation. As it turns out, this construction effectively emulates a left/right factorization of the scattering amplitude and introduces a relative sign flip in the propagator for the sector-split target space coordinates. $N$-point tree-level amplitudes can be easily shown to coincide with the results of Siegel et al.