Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-08-28
J.Math.Phys. 43 (2002) 4180-4201
Physics
High Energy Physics
High Energy Physics - Theory
Harvmac, 31 pages; typos corrected, symmetry analysis made more precise, conclusion expanded, and references added
Scientific paper
10.1063/1.1489070
A new way of constructing fusion bases (i.e., the set of inequalities governing fusion rules) out of fusion elementary couplings is presented. It relies on a polytope reinterpretation of the problem: the elementary couplings are associated to the vertices of the polytope while the inequalities defining the fusion basis are the facets. The symmetry group of the polytope associated to the lowest rank affine Lie algebras is found; it has order 24 for $\su(2)$, 432 for $\su(3)$ and quite surprisingly, it reduces to 36 for $\su(4)$, while it is only of order 4 for $\sp(4)$. This drastic reduction in the order of the symmetry group as the algebra gets more complicated is rooted in the presence of many linear relations between the elementary couplings that break most of the potential symmetries. For $\su(2)$ and $\su(3)$, it is shown that the fusion-basis defining inequalities can be generated from few (1 and 2 respectively) elementary ones. For $\su(3)$, new symmetries of the fusion coefficients are found.
Bégin L.
Cummins C.
Lapointe Luc
Mathieu Pierre
No associations
LandOfFree
Fusion bases as facets of polytopes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fusion bases as facets of polytopes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fusion bases as facets of polytopes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-101823