Long, partial-short, and special conformal fields

Abstract

In the framework of metric-like approach, totally symmetric arbitrary spin bosonic conformal fields propagating in flat space-time are studied. Depending on the values of conformal dimension, spin, and dimension of space-time, we classify all conformal field as long, partial-short, short, and special conformal fields. An ordinary-derivative (second-derivative) Lagrangian formulation for such conformal fields is obtained. The ordinary-derivative Lagrangian formulation is realized by using double-traceless gauge fields, Stueckelberg fields, and auxiliary fields. Gauge-fixed Lagrangian invariant under global BRST transformations is obtained. The gauge-fixed BRST Lagrangian is used for the computation of partition functions for all conformal fields. Using the result for the partition functions, numbers of propagating D.o.F for the conformal fields are also found.

LaTeX-2e, 30 pages v2: Typos in eqs. (5.23), (5.24), (7.25) (7.49) corrected

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• On the structure of the conformal higher-spin wave operators
• Conformal Higher-Spin Gravity: Linearized Spectrum = Symmetry Algebra
• 3d conformal fields with manifest $sl(2,\mathbb{C})$
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space
• Scale and Conformal Invariance on (A)dS