$Sp(8)$ invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations

Abstract

We discuss twistor-like interpretation of the $Sp(8)$ invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian $Sp(8)/P$ which is the generalized space-time in this framework. The correspondence space $\mathbf{C}$ is $SpH(8)/PH$ where $SpH(8)$ is the semidirect product of $Sp(8)$ with Heisenberg group $\HG$ and $PH$ is some quasiparabolic subgroup of $SpH(8)$. Spaces of functions on $Sp(8)/P$ and $SpH(8)/PH$ consist of $Q_P$ closed functions on $Sp(8)$ and $Q_{PH}$ closed functions on $SpH(8)$, where $Q_P$ and $Q_{PH}$ are canonical BRST operators of $P$ and $PH$. The space of functions on the generalized twistor space $\mathbf{T}$ identifies with the $SpH(8)$ Fock module. Although $\mathbf{T}$ cannot be realized as a homogeneous space, we find a nonstandard $SpH(8)$ invariant BRST operator $\QQ$ $(\QQ^2 =0)$ that gives rise to an appropriate class of functions via the condition $\QQ f=0$ equivalent to the unfolded higher--spin equations. The proposed construction is manifestly $Sp(8)$ invariant, globally defined and coordinate independent. Its Minkowski analogue gives a version of twistor theory with both types of chiral spinors treated on equal footing. The extensions to the higher rank case with several Heisenberg groups and to the complex case are considered. A relation with Riemann theta functions, that are $\QQ$-closed, is discussed.

26 pages, clarifications and references added, typos corrected

References in corpus (7)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• On Conformal, SL(4,R) and Sp(8,R) Symmetries of 4d Massless Fields
• Higher Spin Fields in Siegel Space, Currents and Theta Functions
• E_{11} and Higher Spin Theories
• New Model of Higher-Spin Particle

Cited by in corpus (17)

• Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory
• Families of exact solutions to Vasiliev's 4D equations with spherical, cylindrical and biaxial symmetry
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. I. Bosonic fields
• Conformal higher spin scattering amplitudes from twistor space
• Conformal geometry and (super)conformal higher-spin gauge theories
• Conformal Higher Spin Theory and Twistor Space Actions
• Higher Spins in Hyper-Superspace
• Higher Spins in Hyperspace
• Planar solutions of higher-spin theory I: free field level
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• On Tensorial Spaces and BCFW Recursion Relations for Higher Spin Fields
• BRST Analysis of the Supersymmetric Higher Spin Field Models
• Twistors and supertwistors for exceptional field theory
• Unfolded Formulation of 4d Yang-Mills Theory
• Correlation Functions of Sp(2n) Invariant Higher-Spin Systems
• Scattering amplitudes as multi-particle higher-spin charges in the correspondence space
• Higher-spin fields and charges in the periodic spinor space