GL(2,R) dualities in generalised Z(2) gauge theories and Ising models

Details GL(2,R) dualities in generalised Z(2) gauge theories and Ising models GL(2,R) dualities in generalised Z(2) gauge theories and Ising models

2007-01-09

arxiv.org/abs/hep-th/0701075v1

JHEP 0703:081,2007

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 4 figures

Scientific paper

10.1088/1126-6708/2007/03/081

We study a class of duality transformations in generalised Z(2) gauge theories and Ising models on two- and three-dimensional compact lattices. The theories are interpreted algebraically in terms of the structure constants of a bidimensional vector space H with algebra and coalgebra structures, and it is shown that for any change of basis in H there is a related symmetry between such models. The classical Kramers and Wannier dualities are described as special cases of these transformations. We derive explicit expressions for the relation between partition functions on general finite triangulations for these cases, extending results known for square and cubic lattices in the thermodynamical limit. A class of symmetry transformations in which the gauge coupling changes continuously is also studied in two dimensions.

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