Dual resonant amplitudes from Drinfel'd twists

TL;DR

This paper introduces a new family of dual resonant four-point tachyon amplitudes derived from Drinfel'd twists, with some exhibiting good ultraviolet behaviour in high-energy scattering regimes, based on $q$-deformed worldsheet CFTs.

Contribution

It presents a novel construction of dual resonant amplitudes using Drinfel'd twists and explores their ultraviolet properties within $q$-deformed conformal field theories.

Findings

Identification of a sub-family with well-defined UV behaviour

Connection to $q$-deformed worldsheet CFTs and quantum groups

Discussion on the $q$-deformations of Veneziano and Coon amplitudes

Abstract

We postulate the existence of a family of dual resonant, four-point tachyon amplitudes derived using invertible coproduct maps called Drinfel'd twists. A sub-family of these amplitudes exhibits well-defined ultraviolet behaviour, namely in the fixed angle high-energy and Regge scattering regimes. This discovery emerges from a systematic study of the set of observables that can be constructed out of $q$-deformed worldsheet CFTs with the underlying conformal group being the quantum group $SU(1,1)_q$. We conclude our analysis by discussing the possibility (or the lack thereof) of known $q$-deformations of the Veneziano amplitude as an observable in such theories, in particular, the Coon amplitude.