Topology and higher dimensional representations

Details Topology and higher dimensional representations Topology and higher dimensional representations

2009-05-22

arxiv.org/abs/0905.3586v2

JHEP 0908:084,2009

Physics

High Energy Physics

High Energy Physics - Lattice

14 pages, 7 figures; discussion and references added

Scientific paper

10.1088/1126-6708/2009/08/084

SU(3) gauge theory in the 2-index symmetric (sextet) and fundamental representations is considered in symmetric and periodic boxes. Using the overlap formulation in the quenched approximation it is shown that the topological charge obtained from the sextet index theorem always leads to an integer value and agrees with the charge obtained from the fundamental index theorem in the continuum. At larger lattice spacing configurations exist with fractional topological charge if the sextet index is used but these are lattice artifacts and the probability of finding such a configuration rapidly approaches zero. By considering the decomposition of the sextet representation with respect to an SU(2) subgroup it is shown that the SU(2) adjoint index theorem leads to integer charge as well. We conclude that the non-zero value of the bilinear gaugino condensate in N=1 super-Yang-Mills theory cannot be attributed to configurations with fractional topological charge once periodic boundary conditions are imposed.

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