Speaker
Description
Understanding the microscopic origin of confinement and the other gapped phases in four-dimensional Yang–Mills theory remains a central challenge. The Wilson–’t Hooft classification constrains these phases through the behavior of electric and magnetic line operators. The Cardy–Rabinovici model provides an Abelian setting in which to study confinement, oblique confinement, and duality. In our previous work, we formulated its two-dimensional reduction on a modified Villain lattice and studied its exact dualities, symmetries, and phase structure. That analysis also highlighted a limitation: the Abelian model does not realize every gapped phase allowed by the Wilson–’t Hooft classification.
In this talk, We will discuss an approach based on a semi-Abelian theory motivated by compactifying four-dimensional Yang–Mills theory. Its low-energy description contains Abelian holonomies together with permutations of their color eigenvalues. This structure admits twist vortices associated with those permutations. We will examine how these defects and their screening affect the vacuum structure, and whether they can provide a route to gapped phases inaccessible in the Abelian Cardy–Rabinovici model.