CFT adapted approach to massless fermionic fields, AdS/CFT, and fermionic conformal fields

Abstract

Fermionic totally symmetric arbitrary spin massless fields in AdS space of dimension greater than or equal to four are studied. Using Poincaré parametrization of AdS space, CFT adapted gauge invariant formulation for such fields is developed. We demonstrate that the curvature and radial coordinate contributions to Lagrangian and gauge transformation of the AdS fields can be expressed in terms of ladder operators. Covariant and modified de Donder gauge conditions are proposed. The modified de Donder gauge leads to decoupled equations of motion which can easily be solved in terms of the Bessel function. The AdS/CFT correspondence for conformal current and shadow field and the respective normalizable and non-normalizable modes of fermionic massless AdS field is studied. The AdS field is considered by using the modified de Donder gauge which simplifies considerably the study of AdS/CFT correspondence. We show that on-shell leftover gauge symmetries of bulk massless field are related to gauge symmetries of boundary conformal current and shadow field. We compute the bulk action on solution of the Dirichlet problem and obtain two-point gauge invariant vertex of shadow field. Also we shown that the UV divergence of the two-point gauge invariant vertex gives higher-derivative action of fermionic conformal field.

34 pages, LaTeX-2e, v2: Typos in Eq.(2.35) corrected. References added. arXiv admin note: text overlap with arXiv:1110.3749

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Cited by in corpus (10)

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• Higher-Spin Theory and Space-Time Metamorphoses
• Boundary values of mixed-symmetry massless fields in AdS space
• Higher Spins in Hyper-Superspace
• Supertwistor formulation for massless superparticle in $Ad{S}_5\times S^5$ superspace
• Ambitwistors, oscillators and massless fields on $Ad{S}_5$
• Lagrangian formulation of massive fermionic higher spin fields on a constant electromagnetic background
• The Involutive System of Higher-Spin Equations
• Higher-Rank Fields and Currents
• Scalar field on AdS: quantum one loop "in one line"