Toward a 3d Ising Model with a weakly coupled string dual

It has long been expected that the 3d Ising model can be thought of as a string theory, where one interprets the domain walls that separate up spins from down spins as two-dimensional string worldsheets. I will revisit this “string theory” from the modern point of view of higher form symmetries. The usual Ising Hamiltonian measures the area of these domain walls; as there is no explicit dependence on the genus of the domain walls, it can be thought of as a string theory with string coupling equal to unity. I discuss how to add new local terms to the Ising Hamiltonian that further weight each spin configuration by a factor depending on the genus of the corresponding domain wall, resulting in a new 3d Ising model that has a tunable bare string coupling g_s. I will use a combination of analytical and numerical methods to analyze the phase structure of this model as g_s is varied. I will also describe statistical properties of the topology of worldsheets and speculate on the prospects of using this new deformation at weak string coupling to find a worldsheet description of the 3d Ising transition.