Horizontal supersymmetry and Weyl character formulae

The concept of a horizontal supersymmetry over a reductive coset space, G/H, is developed. By an adaptation of the Borel-Weil theory to vector bundles, an alternate form of the Weyl character formula is obtained through a supersymmetric index calculation. This is then shown to produce a relation bet...

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Published inNuclear physics. B Vol. 359; no. 1; pp. 75 - 90
Main Authors Cleveland, Michael G., Pritchett, Tim
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 29.07.1991
Elsevier
Subjects
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Physics
Theory of quantized fields
Supersymmetry
Quantum field theory
Manifold
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Summary:The concept of a horizontal supersymmetry over a reductive coset space, G/H, is developed. By an adaptation of the Borel-Weil theory to vector bundles, an alternate form of the Weyl character formula is obtained through a supersymmetric index calculation. This is then shown to produce a relation between the character of an element of the group G and the character in the appropriate representation for the corresponding element of the subgroup H. The example of SU(3)/SU(2) × U(1) for the 3 representation is studied in detail.
ISSN:0550-3213
1873-1562
DOI:10.1016/0550-3213(91)90293-7