Abstract
Higher spin field theory on AdS(4) is defined by lifting the minimal conformal sigma model in three-dimensional flat space. This allows to calculate the masses from the anomalous dimensions of the currents in the sigma model. The Goldstone boson field can be identified.
Highlights
We consider the higher spin field theory constructed on AdS(4)space by lifting of the O(N) vector minimal sigma model from R(3)[1]
It results a nonlocal interacting renormalized QFT denoted HS(4) and defined by its n-point functions which can each be computed by a 1/N expansion. Such AdS field theory has the unconventional property that mass renormalizations of the fundamental fields and composite fields can be calculated perturbatively. This is made possible by the fact that the corresponding flat conformal field theory permits to calculate the anomalous part η of the conformal dimension ∆ by 1/N expansion and that the mass m2 of the AdS field and ∆ of the dual conformal field are related, e.g. for symmetric tensor fields of rank l by m2l = ∆(∆ − d) − (l − 2)(d + l − 2)
Lifting of the flat conformal field theory is done with the bulk-to-boundary propagator
Summary
We consider the higher spin field theory constructed on AdS(4)space by lifting of the O(N) vector minimal sigma model from R(3)[1]. It results a nonlocal interacting renormalized QFT denoted HS(4) and defined by its n-point functions which can each be computed by a 1/N expansion. In the minimal sigma model the operator product of the current J(l) with the scalar field α contains by expansion the currents J(l,t) with dimension d − 2 + l + 2t, t ∈ N, (in the free field limit). The starting point for a calculation of the masses m2l is the AdS four-point function
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