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Article overview
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$Sp(8)$ invariant higher spin theory, twistors and geometric BRST formulation of unfolded field equations | | O.A. Gelfond
; M.A.Vasiliev
; | | Date: |
15 Jan 2009 | | Abstract: | We discuss twistor-like interpretation of the $Sp(8)$ invariant formulation
of 4d massless fields in ten-dimensional Lagrangian Grassmannian space
$Sp(8)/P$ which is the generalized space-time in this framework. The
correspondence space $C$ 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 $QQ_P $ closed functions on $Sp(8)$ and $QQ_{PH} $ closed functions on
$SpH(8)$, where $QQ_P $ and $QQ_{PH}$ are canonical BRST operators of $P$ and
$PH$. The space of functions on the generalized twistor space $T$ identifies
with the $SpH(8)$--Fock module. Although $T$ 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 relationship with Riemann theta functions, that
are ${}^mathbb{C}QQ$-closed, is discussed. | | Source: | arXiv, 0901.2176 | | Services: | Forum | Review | PDF | Favorites | |
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