Speaker: Carlotta Marchis (University of Graz)
Title: Dualization of non-abelian lattice field theories with abelian color cycles (ACCs)
Abstract: A new approach to dualize non-abelian lattice field theories is presented. Starting from the Wilson action, one explicitly rewrites the trace and matrix multiplications leading to a decomposition of the action into a sum over abelian color cycles (ACCs). These objects are complex numbers that on the lattice have the geometrical interpretation of paths in color space around plaquettes. The decomposed action enables the factorization of the Boltzmann weight into local factors which are then expanded, thus introducing new integer valued variables, so-called dual variables, which will substitute the conventional degrees of freedom in the description of the system after the integration of the latter. The ACC technique is a very general method, and in this talk the examples of application to SU(2) and SU(3) pure gauge theories are discussed. Moreover it will be shown how the approach can be easily extended to the theory with matter in the case of SU(2).