Six-dimensional supermultiplets from bundles on projective spaces
The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to P1xP3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
February 2025
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| In: |
Communications in mathematical physics
Year: 2025, Jahrgang: 406, Heft: 2, Pages: 1-52 |
| ISSN: | 1432-0916 |
| DOI: | 10.1007/s00220-024-05176-3 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s00220-024-05176-3 Verlag, kostenfrei, Volltext: https://link.springer.com/article/10.1007/s00220-024-05176-3 
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| Verfasserangaben: | Fabian Hahner, Simone Noja, Ingmar Saberi, Johannes Walcher |
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| 520 | |a The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to P1xP3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {P}<^>1 \times \mathbb {P}<^>3$$\end{document}. We use this fact, together with the pure spinor superfield formalism, to study supermultiplets in six dimensions, starting from vector bundles on projective spaces. We classify all multiplets whose derived invariants for the supertranslation algebra form a line bundle over the nilpotence variety; one can think of such multiplets as being those whose holomorphic twists have rank one over Dolbeault forms on spacetime. In addition, we explicitly construct multiplets associated to natural higher-rank equivariant vector bundles, including the tangent and normal bundles as well as their duals. Among the multiplets constructed are the vector multiplet and hypermultiplet, the family of O(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {O}}(n)$$\end{document}-multiplets, and the supergravity and gravitino multiplets. Along the way, we tackle various theoretical problems within the pure spinor superfield formalism. In particular, we give some general discussion about the relation of the projective nilpotence variety to multiplets and prove general results on short exact sequences and dualities of sheaves in the context of the pure spinor superfield formalism. | ||
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