Probing center vortices and deconfinement in $\mathrm{SU}(2)$ lattice gauge theory with persistent homology

Understand

We investigate the use of persistent homology, a tool from topological data analysis, as a means to detect and quantitatively describe center vortices in $\mathrm{SU}(2)$ lattice gauge theory in a gauge-invariant manner.

• We provide evidence for the sensitivity of our method to vortices by detecting a vortex explicitly inserted using twisted boundary conditions in the deconfined phase.
• This inspires the definition of a new phase indicator for the deconfinement phase transition.
• We also construct a phase indicator without reference to twisted boundary conditions using a simple $k$-nearest neighbours classifier.