Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-01-03
Nucl.Phys.B794:324-347,2008
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, 2 figures
Scientific paper
10.1016/j.nuclphysb.2007.11.004
A large class of orbifold quiver gauge theories admits the action of finite Heisenberg groups of the form \prod_i Heis(Z_{q_i} x Z_{q_i}). For an Abelian orbifold generated by \Gamma, the Z_{q_i} shift generator in each Heisenberg group is one cyclic factor of the Abelian group \Gamma. For general non-Abelian \Gamma, however, we find that the shift generators are the cyclic factors in the Abelianization of \Gamma. We explicitly show this for the case \Gamma=\Delta(27), where we construct the finite Heisenberg group symmetries of the field theory. These symmetries are dual to brane number operators counting branes on homological torsion cycles, which therefore do not commute. We compare our field theory results with string theory states and find perfect agreement.
Burrington Benjamin A.
Liu James T.
Pando Zayas Leopoldo A.
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