Beyond Wilson? Carroll from current deformations

TL;DR

This paper explores how high-energy deformations of 2D scalar field theories can lead to a transition from relativistic conformal symmetry to Carrollian symmetry, revealing new quantum flows and symmetry structures at extreme energies.

Contribution

It demonstrates how current-current deformations induce a transition from conformal to Carrollian symmetries in 2D scalar theories at high energies, highlighting novel quantum flows.

Findings

Deformation of conformal algebra to Carrollian algebra at high energies

Distinct quantum flows driven by symmetric and antisymmetric currents

Emergence of Carrollian CFTs from current-current deformations

Abstract

At extreme energies, both low and high, the spacetime symmetries of relativistic quantum field theories (QFTs) are expected to change with Galilean symmetries emerging in the very low energy domain and, as we will argue, Carrollian symmetries appearing at very high energies. The formulation of Wilsonian renormalisation group seems inadequate for handling these changes of the underlying Poincare symmetry of QFTs and it seems unlikely that these drastic changes can be seen within the realms of relativistic QFT. We show that contrary to this expectation, changes in the spacetime algebra occurs at the very edges of parameter space. In particular, we focus on the very high energy sector and show how bilinears of $U(1)$ currents added to a two dimensional (massless) scalar field theory deform the relativistic spacetime conformal algebra to conformal Carroll as the effective coupling of the deformation is dialed to infinity. We demonstrate this using both a symmetric and an antisymmetric current-current deformation for theories with multiple scalar fields. These two operators generate distinct kinds of quantum flows in the coupling space, the symmetric driven by Bogoliubov transformations and the antisymmetric by spectral flows, both leading to Carrollian CFTs at the end of the flow.