U(N) spinning particles and higher spin equations on complex manifolds

Abstract

Guided by a spinning particle model with U(N)-extended supergravity on the worldline we derive higher spin equations on complex manifolds. Their minimal formulation is in term of gauge fields which satisfy suitable constraints. The latter can be relaxed by introducing compensator fields. There is an obstruction to define these systems on arbitrarily curved spaces, just as in the usual theory of higher spin fields, but we show how to couple them to Kaehler manifolds of constant holomorphic curvature. Quite interestingly, the first class gauge algebra defining the U(N) particles on these manifolds is quadratic and realizes the zero mode sector of certain nonlinear U(N) superconformal algebras introduced sometimes ago by Bershadsky and Knizhnik in 2D.

26 pages

References in corpus (5)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• An Introduction to Free Higher-Spin Fields
• Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras
• The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
• BiHermitian Supersymmetric Quantum Mechanics

Cited by in corpus (2)

• Detours and Paths: BRST Complexes and Worldline Formalism
• Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS_d space