Effective Lagrangians for low-dimensional descendants of N = 2 4D supersymmetric Yang-Mills theories

by A. SMILGA (University of Nantes)

Thursday 27 Feb 2003, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

We construct effective Lagrangians for the theories obtained by dimensional reduction of N=2 4D supersymmetric Yang-Mills theories in 3, 2, and 1 dimensions for any gauge group. The 3D effective theories represent hyper-Kahlerian sigma models. The dimension of the target space is 4r (r is the rank of the group). We write explicit perturbatively exact expressions for the metric for all groups. The 2D effective Lagrangians are sigma models enjoying N=4 supersymmetry, but they are not hyper-Kahlerian, but rather belong to the class of "twisted" sigma models developped by Gates, Hull, and Rocek. Finally, the effective (0+1) theories are N=4 SQM sigma models living on a target space of dimension 5r. They represent a generalisation of the model suggested earlier by Diaconescu and Entin. We establish a genetic relationship between effective Lagrangians in different dimensions. In particular, the relationship of the low-dimensional Lagrangians to 4-dimensional beta function is explored.