Effective action in a higher-spin background

Abstract

We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.

One-loop effective actions and higher spins. Part II

“…Other topics, such as the discussion of the ambiguities inherent in the choice of the conserved currents in the initial matter model, will be included in a subsequent article. This is a good point to mention that our research is indebted to several preexisting works, in particular with [17][18][19] as far as the inspiration is concerned, with [20][21][22][23][24][25][26][27][28][29] as far as the methods are concerned and with [4,5,[30][31][32][33][34][35][36][37][38][39][40][41] for HS theories. Other papers of ours, related to the present one are, beside [1,42,43].…”

“…As said above, the interest of [24] is limited to conformal higher spin theories. Later on Bekaert et al [25] have revisited and extended this method, but always considering a massless scalar.…”

“…As compared to [24,25], our method is based on Feynman diagrams together with a considerable technical improvement in computing the latter. In particular, in the present draft, we have extended our previous results in [1] to mixed spin terms, which also turn out to be always made up of a nonlocal transverse part and a local non-transverse one.…”

“…In particular, in the present draft, we have extended our previous results in [1] to mixed spin terms, which also turn out to be always made up of a nonlocal transverse part and a local non-transverse one. The main difference with the methods of [24,25], is that we deal with massive scalar and fermion theories coupled to external sources. The introduction of a mass is important because it allows us to intercept not only the conformal higher spin kinetic terms which can be found in [66], but also the Fronsdal equations for symmetric fields which appear in [4,5].…”

Massive fermion model in 3d and higher spin currents

“…This paper is devoted to the free massive fermion model in 3d coupled to various sources. Unlike the free massless fermion, [9], this model has not been extensively studied, although examples of research in this direction exist, see for instance [10][11][12] and also [4], and for the massless scalar model [13]. Its prominent property, as opposed to the massless one, 1 is that the fermion mass parameter m breaks parity invariance, and this feature has nontrivial consequences even when m → 0.…”