The physical observer II: Gauge and diff anomalies

TL;DR

This paper explores how incorporating a quantum physical observer into field theory leads to novel gauge and diffeomorphism anomalies, which depend on the observer's trajectory and have implications for quantum gravity in four dimensions.

Contribution

It introduces a new class of gauge and diff anomalies arising from the observer's quantum dynamics, highlighting their dependence on spacetime trajectories.

Findings

New gauge and diff anomalies depend on observer trajectories

Anomalies are absent in standard QFT without observer trajectory

Anomaly cancellation constrains spacetime to four dimensions

Abstract

In a companion paper we studied field theory in the presence of a physical observer with quantum dynamics. Here we describe the most striking consequence of this assumption: new gauge and diff anomalies arise. The relevant cocycles depend on the observer's spacetime trajectory and can hence not appear in QFT, where this quantity is never introduced. Diff anomalies necessarily arise in every locally nontrivial, non-holographic theory of quantum gravity. Cancellation of the divergent parts of the anomalies only works if spacetime has four dimensions.