Lattice supersymmetry with Hopf algebra for the link approach

Details Lattice supersymmetry with Hopf algebra for the link approach Lattice supersymmetry with Hopf algebra for the link approach

2009-10-16

arxiv.org/abs/0910.3149v1

PoS LAT2009:047,2009

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, contribution to The XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beiji

Scientific paper

A formalism of lattice supersymmetry based on a lattice-deformed superalgebra which was originally introduced in the link approach formulation is presented. We propose that the superalgebra can in fact be identified as a Hopf algebra, showing all the Hopf algebra axioms and consistencies are satisfied with explicit formulae. In particular, the "deformed" Leibniz rules proposed in the original link approach are now built in the coproduct structure of the Hopf algebra. Fields in this scheme, as representations of the Hopf algebra, are found to obey a kind of mildly deformed statistics, which is interpreted as a braiding strucutre. We can then construct, at least perturbatively, the corresponding lattice field theory, which has the Hopf algebraic symmetry with the deformed statistics, as an example of braided quantumm field theory formulated by Oeckl.

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