Higher laminations, webs and N=2 line operators

Understand

A detailed study of half-BPS line operators of higher rank 4d N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a bordered Riemann surface with full marked points is performed.

• Geometrically, each 4d UV line operator is represented by an irreducible bipartite web formed by three junctions on Riemann surface, and such web structure is called higher lamination.
• Algebraically, the space of UV line operators is identified with the integral tropical a coordinates of the corresponding PGL(N,C) local system, and the space of IR line operator is identified with the cluster X coordinates of SL(N.C) local system.
• The expectation value of UV line operator at Coulomb branch parameterized by X coordinates is calculated, and the result is a positive Laurent polynomial in X.