DDF amplitudes are lightcone amplitudes and the naturalness of Mandelstam map

TL;DR

This paper demonstrates that on-shell DDF amplitudes are equivalent to lightcone amplitudes and reveals the natural emergence of Mandelstam maps with precise normalization, highlighting their intrinsic connection to DDF states.

Contribution

It establishes the intrinsic link between DDF and lightcone amplitudes and provides an explicit formula for conformal transformations of generic vertices in free theories.

Findings

On-shell DDF amplitudes are equivalent to lightcone amplitudes.

Mandelstam maps naturally emerge with proper normalization.

Explicit conformal transformation formula for generic vertices.

Abstract

We show that on shell DDF amplitudes are on shell lightcone amplitudes and that Mandelstam maps emerge naturally with a precise normalization and are intrinsic to the DDF states. Off shell DDF and Mandelstam amplitudes \`a la Kaku-Kikkawa differ. Underway we give a very explicit formula for the conformal transformation of a generic vertex in the form of a compact generating function for free theories.