Evolving Center-Vortex Loops

Figure 5

(a) plots of Δ_𝑀,COM(𝜏) for 𝑀=3,…,8 when evaluated with the action 𝑆_𝑀=(𝐿(𝜏)²/𝐴(𝜏))(1+(𝑐_𝑀(𝜏)/𝐿(𝜏))). Notice the rapid generation of an uncertainty in the COM position under the flow and its saturation when approaching the conformal limit 𝜏↗𝑇. There is also a saturation of this limiting value with a growing ensemble size. (b) plots of Δ_𝑀,COM(𝜏) for 𝑀=3,…,8 when evaluated with the action 𝑆_𝑀=(𝐿(𝜏)²/𝐴(𝜏))(1+𝑐_𝑀(𝜏)/𝐴(𝜏)). Notice the qualitative agreement with the results displayed in (a).

(a)

(b)