Symmetries of Toric Duality

Details Symmetries of Toric Duality Symmetries of Toric Duality

2002-05-15

arxiv.org/abs/hep-th/0205144v3

JHEP 0212 (2002) 076

Physics

High Energy Physics

High Energy Physics - Theory

33+1 pages, 13 figures; References and Figures Updated

Scientific paper

10.1088/1126-6708/2002/12/076

This paper serves to elucidate the nature of toric duality dubbed in hep-th/0003085 in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally leads to monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and ``node'' symmetries of the quiver and superpotential and how they are intimately related to the isometry of the background geometry, as well as how in certain cases complicated superpotentials can be derived by observations of the symmetries alone.

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