2-Form U(1) Spin Liquids: A Classical Model and Quantum Aspects

In this work I introduce a novel class of 3D spin liquids called 2-form U(1) spin liquids. These are described by emergent 2-form U(1) gauge fields, whose charged excitations are strings rather than particles. We construct an Ising model on the pyrochlore lattice which realizes the classical version of this spin liquid and discuss how to perturbatively map transverse exchange terms to a 2-form U(1) lattice gauge theory, potentially realizing a quantum 2-form U(1) spin liquid. This gauge theory suffers from a confinement instability due to magnetic instantons, the same mechanism that destabilizes 1-form U(1) gauge theory in 2D (the Polyakov mechanism), and we discuss some interesting directions this might lead in, such as a generalization of the Dirac spin liquid (2D U(1) gauge theory plus fermions) to 3D.