HEP Theory Journal Club

q-CFTs from Quantum Groups

Brown University

The uniqueness of the Veneziano amplitude has attracted much theoretical attention since its inception in the 1960s. While there have been proposals for various deformations to the Veneziano amplitude that satisfy the bootstrap constraints, a worldsheet realisation of such models has remained elusive. In this talk, we shall outline a systematic construction of q-deformed CFTs whose underlying conformal group is the quantum group SU(1,1)_q. After reviewing existing literature on the set of observables emanating from such q-CFTs, we will discuss the construction of q-deformed amplitudes derived using invertible coproduct maps called Drinfel’d twists. Upon a suitable analytic continuation, we show that these twisted amplitudes are manifestly dual resonant. We will conclude by discussing a potential worldsheet realisation (or the lack thereof) of a particular q-deformation of the Veneziano amplitude, the Coon amplitude, in the space of such worldsheet q-CFTs. The talk will be based on 2309.07214.