A generating function for the cubic interactions of higher spin fields

Abstract

We present an off-shell generating function for all cubic interactions of Higher Spin gauge fields constructed in [1]. It is a generalization of the on-shell generating function proposed in [2], is written in a very compact way, and turns out to have a remarkable structure.

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…[37,38], while, in metric-like approach, in refs. [39][40][41]. In BRST approach, cubic vertices involving arbitrary spin massless and massive fields were derived in ref.…”

“…Operator G 3 (C.40) is a secondorder differential operator with respect to the variable z 3 . To simplify the G 3 , we use the transformation 41) and verify that, on the vertex V (6) , operator G 3 (C.40) is realized as…”

“…Realization on V (7) . In order to remove the dependence of the G 1 on the variable z 2 (D.39) and the dependence of the G 2 on the variable z 1 (D.40) we use the transformation 41) and verify that, on the vertex V (7) , operators G 1 , G 2 (D.39), (D.40) are realized as…”

Higher-spin fermionic gauge fields and their electromagnetic coupling

“…(4.13) cannot be Γ-exact modulo d. Therefore, the candidate C * ξ µ ξ µ is ruled out. However, one finds that 14) thanks to the relation (B.10). Thus, indeed, C * ξ (1) µν ξ (1)µν gets lifted to an a 1 :…”

“…Metsaev's light-cone formulation [10,11] puts restrictions on the number of derivatives in these vertices, and thereby provides a way of classifying them. For bosonic fields, while the complete list of such vertices was given in [12], Noether procedure has been employed in [13][14][15] to explicitly construct off-shell vertices, which do obey the number-of-derivative restrictions. Also, the tensionless limit of string theory gives rise to a set of cubic vertices, which are in one-to-one correspondence with the ones of Metsaev, as has been noticed by Sagnotti-Taronna in [16,17], where generating functions for off-shell trilinear vertices for both bosonic and fermionic fields were presented.…”