Six-dimensional supermultiplets from bundles on projective spaces

Abstract

The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to ${\mathbb{P}}^1\times {\mathbb{P}}^3$. 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 $\mathcal{O}(n)$-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.

63 pages. Comments welcome! v2: substantially improved exposition; to appear in Communications in Mathematical Physics

References in corpus (18)

• Super-Poincare Covariant Quantization of the Superstring
• D-branes, Categories and N=1 Supersymmetry
• Towards Covariant Quantization of the Supermembrane
• On maximally supersymmetric Yang-Mills theories
• D=11 supergravity with manifest supersymmetry
• D-Branes on Calabi-Yau Manifolds
• Pure spinor superfields -- an overview
• Six-dimensional Supergravity and Projective Superfields
• Towards a manifestly supersymmetric action for 11-dimensional supergravity
• Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
• Quantum Field Theory as Effective BV Theory from Chern-Simons
• Maximally twisted eleven-dimensional supergravity
• Perspectives on the pure spinor superfield formalism
• Pure spinor superspace action for D=6, N=1 super-Yang-Mills theory
• New superconformal multiplets and higher derivative invariants in six dimensions
• On the Geometry of Forms on Supermanifolds
• A Note on Super Koszul Complex and the Berezinian
• Non-conformal supercurrents in six dimensions

Cited by in corpus (1)

• Twisting BFSS & IKKT