Abstract
We determine the Feynman rules for the minimal type A higher-spin gauge theory on AdSd+1 at cubic order. In particular, we establish the quantum action at cubic order in de Donder gauge, including ghosts. We also give the full de Donder gauge propagators of higher-spin gauge fields and their ghosts. This provides all ingredients needed to quantise the theory at cubic order.
Highlights
In spite of the above remarkable efforts, all attempts are being confronted with one and the same conceptual subtlety, which is intimately related to the definition of a non-local extension of the classical field theoretic deformation problem that lies at the basis of Einstein General Relativity and QFT
Beyond the cubic order a proper extension of the functional class of local Lagrangian functionals and equations of motion is currently lacking. This goes hand in hand with the proliferation of infinitely many explicitly non-local off-shell solutions to the Noether procedure,1 which lead to one and the same observable defined by AdS/CFT correspondence. It was further argued in [51] that no proper extension of the functional space of non-localities is possible in a properly defined generalised field theoretic context and that one may have to resort to String Theory, i.e. beyond the realm of field theory, to achieve a proper definition of higher-spin theories
In the same way as it is possible to enlarge the functional domain to define an integral transform, the key question is about a clever choice of regularity conditions which ensure a proper independent definition of both the boundary and bulk sides of the duality. For these reasons it is important to push beyond tree-level, and investigate quantum properties of higher-spin gauge theories independently on both the bulk and boundary sides to test the degree of non-localities
Summary
In this work we determine the gauge fixed path integral of the minimal type A higherspin gauge theory on AdSd+1 up to cubic order fluctuations, together with associated propagators in the same gauge. The bulk-to-bulk propagator for a spin-s Fronsdal field in de Donder gauge is given by. We determine the ghost bulk-to-boundary propagators in section 4.1.2, which in the ambient space formalism read. These are to accompany the bulk-to-boundary propagators for the associated spin-s gauge fields, which were determined by Mikhailov in [79]. On the conformal boundary of AdSd+1, operators of non-trivial spin can likewise be encoded in generating function notation.
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