Emergent Anyon Distribution in the Unruh Effect

TL;DR

The work investigates the Unruh–DeWitt detector coupled to a scalar primary operator in a $d$-dimensional conformal field theory and shows that the detector's power spectrum at the Unruh temperature $T=a/(2\pi)$ takes the form of a thermal distribution for $(1+1)$-dimensional anyons with statistical parameter $\kappa=2\Delta$, where $\Delta$ is the operator's scaling dimension. This yields a continuous interpolation between Bose–Einstein and Fermi–Dirac statistics, generalizing Takagi's inversion and linking the analytic structure of conformal correlators to anyon-like exchange. The results provide a geometric interpretation via the Plancherel measure on hyperbolic space and highlight a deep connection between statistics, conformal symmetry, and observer kinematics in accelerated frames.

Abstract

We point out that, when the Unruh-DeWitt detector couples to a scalar primary operator of $d$-dimensional conformal field theory, the detector's power spectrum generally obeys the thermal distribution for $(1+1)$-dimensional anyons.

Figures (1)

• Figure 1: Typical detector's power spectra. The case $\omega=E_{f}-E_{i}>0$ corresponds to the absorption process while the case $\omega=E_{f}-E_{i}<0$ corresponds to the emission process. Note that the scaling dimension $\Delta$ is bounded below by $(d-2)/2$ in unitary conformal field theories.