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

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Cited by in corpus (21)

• On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
• Maxwell-like Lagrangians for higher spins
• Detours and Paths: BRST Complexes and Worldline Formalism
• Effective action for higher spin fields on (A)dS backgrounds
• Quantum mechanical path integrals in the first quantised approach to quantum field theory
• Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS_d space
• Current Exchanges for Reducible Higher Spin Multiplets and Gauge Fixing
• Half-integer Higher Spin Fields in (A)dS from Spinning Particle Models
• Extended SUSY quantum mechanics: transition amplitudes and path integrals
• Quantum theories of (p,q)-forms
• BRST Detour Quantization
• Generalized Einstein Operator Generating Functions
• Quantum theory of massless (p,0)-forms
• Mixed symmetry Wilson-loop interactions in the worldline formalism
• Six-dimensional one-loop divergences in quantum gravity from the $\mathcal{N}=4$ spinning particle
• Gauge-invariant coefficients in perturbative quantum gravity
• U(N|M) quantum mechanics on Kaehler manifolds
• (p,q)-form Kaehler Electromagnetism
• Quaternionic Kaehler Detour Complexes & N=2 Supersymmetric Black Holes
• $U(N)$ Yang-Mills in non-commutative space time
• U(N) spinning particles and higher spin fields on Kaehler backgrounds