Topological modes in dual lattice models.

Lattice gauge theory with gauge group ZP is reconsidered in four dimensions on a simplicial complex K. One finds that the dual theory, formulated on the dual block complex K̂, contains topological modes which are in correspondence with the cohomology group H2(K̂, ZP ), in addition to the usual dynamical link variables. This is a general phenomenon in all models with single plaquette based actions; the action of the dual theory becomes twisted with a field representing the above cohomology class. A similar observation is made about the dual version of the three dimensional Ising model. The importance of distinct topological sectors is confirmed numerically in the two dimensional Ising model where they are parameterized by H1(K̂, Z2). PACS numbers: 11.15.Ha, 05.50.+q October 1994 DIAS Preprint 94-32 Email: [email protected]