Gauge symmetry from decoupling

TL;DR

This paper explains how gauge symmetries naturally arise from the decoupling of heavy modes in quantum field theories, providing a framework for understanding gauge invariance without explicit constraints.

Contribution

It introduces a formulation of gauge invariant fields for non-linear light degrees of freedom and shows how gauge symmetries can emerge through the renormalization flow.

Findings

Gauge symmetries emerge from decoupling of heavy modes.

Gauge invariance can be formulated without explicit constraints.

Emergence of gauge symmetries relates to mass-like terms in flow equations.

Abstract

Gauge symmetries emerge from a redundant description of the effective action for light degrees of freedom after the decoupling of heavy modes. This redundant description avoids the use of explicit constraints in configuration space. For non-linear constraints the gauge symmetries are non-linear. In a quantum field theory setting the gauge symmetries are local and can describe Yang-Mills theories or quantum gravity. We formulate gauge invariant fields that correspond to the non-linear light degrees of freedom. In the context of functional renormalization gauge symmetries can emerge if the flow generates or preserves large mass-like terms for the heavy degrees of freedom. They correspond to a particular form of gauge fixing terms in quantum field theories.