부산대학교 도서관

We relate two classical dualities in low-dimensional quantum field theory:Kramers-Wannier duality of the Ising and related lattice models in $2$dimensions, with electromagnetic duality for finite gauge theories in $3$dimensions. The relation is mediated by the notion of boundary field theory:Ising models are boundary theories for pure gauge theory in one dimensionhigher. Thus the Ising order/disorder operators are endpoints of Wilson/'tHooft defects of gauge theory. Symmetry breaking on low-energy states reflectsthe multiplicity of topological boundary states. In the process we describelattice theories as (extended) topological field theories with boundaries anddomain walls. This allows us to generalize the duality to non-abelian groups;finite, semi-simple Hopf algebras; and, in a different direction, to finitehomotopy theories in arbitrary dimension.