The state/defect correspondence

Abstract

We formulate a one-to-one correspondence between states and defects for higher-form gauge theories in arbitrary dimensions. The correspondence is not predicated on conformal invariance, as these theories are in general not conformal. Instead, it relies on the existence of infinitely many conserved charges associated with the mixed anomaly of electric and magnetic higher-form symmetries. In $p$-form Maxwell theory, these charges generate an extended Kac-Moody algebra that acts simultaneously on states and on extended operators. We show that this algebra organizes the Hilbert space on $S^p \times S^{d-p-1}$ into highest-weight representations allowing for a direct identification between states and $p$-dimensional defects. In particular, Wilson-'t Hooft defects dressed with local gauge-invariant operators are mapped to squeezed energy eigenstates. We further relate these novel symmetries to higher-spin currents and demonstrate that their construction persists in a class of interacting non-linear electrodynamics theories.