quast_regions

Configuration of finite spacetime subregion 𝑀M inside the global piece 𝑀∪𝑀¯M∪M¯. 𝑀M is delimited by the timelike boundary ΓΓ and partial Cauchy slices Σ1Σ1 and Σ2Σ2. Γ0Γ0 is some distant (possibly asymptotic) boundary. Edge modes on the finite boundary ΓΓ can be realized, for example, via Wilson lines shot in from Γ0Γ0. While from the point of view of the global theory, these edge modes are composite, non-local degrees of freedom, they appear as "new" from the point of view of the subregion theory. They are group-valued degrees of freedom that constitute internal reference frames associated with the structure group of the gauge theory. The edge-frame-dressed observables on ΓΓ thereby describe in a gauge-invariant manner how the subregion 𝑀M relates to its complement 𝑀¯M¯. Edge modes can be viewed as "internalized" external reference frames for the subregion of interest.