Exact Lattice Supersymmetry
Keywords:
lattice supersymmetry, lattice field theory.Abstract
A new formulation of exact supersymmetry on the lattice, based on a different approach to the lattice fermion problem, is reviewed. Supersymmetry is realized on an extended lattice, made of different copies of the original lattice connected by links which are associated to supersymmetry transformations. Each degree of freedom on the lattice corresponds then to more degrees of freedom in the continuum, which however are all part of the same supermultiplet. Species doublers of the lattice fermions find a natural interpretation in this context. Conservation of the sine of the momentum, rather than of the momentum itself, is required, and that leads to a non local theory. Locality is however recovered in the continuum limit. The case of the model with supersymmetry in one dimension is reviewed in some detail.References
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Alessandro D’Adda
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[arXiv:1006.2046 [hep-lat]].
2 A. D’Adda, I. Kanamori, N. Kawamoto
and J. Saito, JHEP 1203 (2012) 043
[arXiv:1107.1629 [hep-lat]].
3 H.B.Nielsen and M.Ninomiya, Absence
of Neutrinos on a Lattice. 1. Proof by Homotopy
Theory, Nucl.Phys. B185 (1981) 20.
4 L.H.Karsten and J.Smit, Lattice Fermions:
Species Doubling, Chiral Invariance, and the
Triangle Anomaly, Nucl.Phys. B183 (1981) 103.
5 A. D’Adda, I. Kanamori, N. Kawamoto and
K. Nagata, Twisted superspace on a lattice, Nucl.
Phys. B 707, 100 (2005) [arXiv:hep-lat/0406029].
6 A. D’Adda, I. Kanamori, N. Kawamoto
and K. Nagata, Exact extended supersymmetry on
a lattice: Twisted N = 2 super Yang-Mills in two
dimensions, Phys. Lett. B 633, 645 (2006)
[arXiv:hep-lat/0507029].
7 F. Cooper and B. Freedman, Aspects Of
Supersymmetric Quantum Mechanics, Annals
Phys. 146, 262 (1983).
Alessandro D’Adda
How to Cite
D’Adda, A. (2012). Exact Lattice Supersymmetry. International Journal of Mathematics and Physics, 3(2), 157–170. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/59
Issue
Section
Theoretical Physics and Plasma Physics
