Perspectives on the pure spinor superfield formalism

Abstract

In this note, we study, formalize, and generalize the pure spinor superfield formalism from a rather nontraditional perspective. To set the stage, we review the notion of a multiplet for a general super Lie algebra, working in the context of the BV and BRST formalisms. Building on this, we explain how the pure spinor superfield formalism can be viewed as constructing a supermultiplet out of the input datum of an equivariant graded module over the ring of functions on the nilpotence variety. We use the homotopy transfer theorem and other computational techniques from homological algebra to relate these multiplets to more standard component-field formulations. Physical properties of the resulting multiplets can then be understood in terms of algebrogeometric properties of the nilpotence variety. We illustrate our discussion with many examples in various dimensions.

arXiv commentv2: updated grant information. 66 pages, 27 tables. Comments welcome!

References in corpus (24)

• Towards Covariant Quantization of the Supermembrane
• $L_{\infty }$-Algebras of Classical Field Theories and the Batalin-Vilkovisky Formalism
• Spinorial cohomology and maximally supersymmetric theories
• Noncommutative homotopy algebras associated with open strings
• On maximally supersymmetric Yang-Mills theories
• D=11 supergravity with manifest supersymmetry
• Off-shell N=2 tensor supermultiplets
• Pure spinor superfields -- an overview
• Scattering Amplitude Recursion Relations in BV Quantisable Theories
• N=8 superfield formulation of the Bagger-Lambert-Gustavsson model
• Algebra+Homotopy=Operad
• On linear sections of the spinor tenfold, I
• Window shifts, flop equivalences and Grassmannian twists
• Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
• De Rham cohomology and homotopy Frobenius manifolds
• Quantum Field Theory as Effective BV Theory from Chern-Simons
• Lectures on Batalin-Vilkovisky formalism and its applications in topological quantum field theory
• Homotopy Algebras via Resolutions of Operads
• Maximally twisted eleven-dimensional supergravity
• Pure spinor superspace action for D=6, N=1 super-Yang-Mills theory
• An off-shell superspace reformulation of D=4, N=4 super-Yang-Mills theory
• Constraints in the BV formalism: six-dimensional supersymmetry and its twists
• Twisting pure spinor superfields, with applications to supergravity
• Massey products and the Golod property for simplicially resolvable rings

Cited by in corpus (8)

• Tree-Level Color-Kinematics Duality from Pure Spinor Actions
• Twisted eleven-dimensional supergravity
• The teleparallel complex
• Six-dimensional supermultiplets from bundles on projective spaces
• The Derived Pure Spinor Formalism as an Equivalence of Categories
• Twisting BFSS & IKKT
• Homotopy representations of extended holomorphic symmetry in holomorphic twists
• Holomorphic field theories and higher algebra