Excitations of Ising Strings on a Lattice

The 3d Ising model in the low temperature (ferromagnetic) phase describes dynamics of two-dimensional surfaces – domain walls between clusters of parallel spins. The Kramers–Wannier duality maps these surfaces into worldsheets of confining strings in the Wegner’s ${\mathbb{Z}}_2$ gauge theory. We study the excitation spectrum of long Ising strings by simulating the ${\mathbb{Z}}_2$ gauge theory on a lattice. We observe a strong mixing between string excitations and the lightest glueball state and do not find indications for light massive resonances on the string worldsheet.