Notes on conformal invariance of gauge fields

Glenn Barnich (1, 2) , Xavier Bekaert (3, 4) , Maxim Grigoriev (5)

1 ULB - Université libre de Bruxelles
2 International Solvay Institutes for Physics and Chemistry [Brussels]
3 LMPT - Laboratoire de Mathématiques et Physique Théorique
4 FDP - Fédération de recherche Denis Poisson
5 LPI RAS - P. N. Lebedev Physical Institute of the Russian Academy of Sciences [Moscow]

In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action, this fact can be used to constrain the latter when knowing the former. We apply this strategy and its generalization for the non-Lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal, unlike the closely related, but less constrained, maximal-depth Fradkin--Tseytlin fields.

Domains: High Energy Physics - Theory [hep-th]

Glenn Barnich, Xavier Bekaert, Maxim Grigoriev. Notes on conformal invariance of gauge fields. Journal of Physics A: Mathematical and Theoretical, 2015, ⟨10.1088/1751-8113/48/50/505402⟩. ⟨hal-01266450⟩