Hausdorff dimension of critical fluctuations in abelian gauge theories

The geometric properties of the critical fluctuations in Abelian gauge theories such as the Ginzburg-Landau model are analyzed in zero background field. Using a dual description, we obtain scaling relations between exponents of geometric and thermodynamic nature. In particular, we connect the anomalous scaling dimension eta of the dual matter field to the Hausdorff dimension D(H) of the critical fluctuations, which are fractal objects. The connection between the values of eta and D(H), and the possibility of having a thermodynamic transition in finite background field, is discussed.

Anomalous scaling dimensions and stable charged fixed point of type-II superconductors

The critical properties of a type-II superconductor model are investigated using a dual vortex representation. Computing the propagators of gauge field A and dual gauge field h in terms of a vortex correlation function, we obtain the values eta(A) = 1 and eta(h) = 1 for their anomalous dimensions. This provides support for a dual description of the Ginzburg-Landau theory of type-II superconductors in the continuum limit, as well as for the existence of a stable charged fixed point of the theory, not in the 3D XY universality class.