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Fierz identities of real Clifford algebras and the number of supercharges. (English) Zbl 0604.22014

One considers supersymmetric gauge theories in quantum mechanics with the bosons and fermions belonging to the adjoint representation of the gauge group. One shows that the supersymmetry constraints are related to the existence of certain Fierz identities for real Clifford algebras. These identities are valid when one has 2, 4, 8, and 16 supercharges.

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
15A66 Clifford algebras, spinors
81T60 Supersymmetric field theories in quantum mechanics
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References:

[1] DOI: 10.1088/0305-4470/9/9/009
[2] DOI: 10.1088/0305-4470/9/9/009
[3] DOI: 10.1016/0370-2693(82)90524-X
[4] DOI: 10.1016/0003-4916(83)90316-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.