Abstract
We propose an approach to compute one-loop corrections to the four-point amplitude in the higher spin gravities that are holographically dual to free O(N), U(N) and USp(N) vector models. We compute the double-particle cut of one-loop diagrams by expressing them in terms of tree level four-point amplitudes. We then discuss how the remaining contributions to the complete one-loop diagram can be computed. With certain assumptions we find nontrivial evidence for the shift in the identification of the bulk coupling constant and 1/N in accordance with the previously established result for the vacuum energy.
Highlights
JHEP11(2019)138 formulation of gravity [9,10,11]; (ii) in any even dimension there is a well-defined higher spin extension of conformal gravity [12,13,14]; (iii) lastly, there exists a chiral higher spin theory in four dimensional flat and AdS spaces that is formulated in the light-cone gauge [15,16,17,18]
We propose an approach to compute one-loop corrections to the four-point amplitude in the higher spin gravities that are holographically dual to free O(N ), U(N ) and USp(N ) vector models
By generalizing to AdS the standard flat space techniques based on unitarity, analyticity and known high-energy behavior of amplitudes, one can compute the singular part of any loop diagram using the on-shell data for lower-loop and lower-point amplitudes and reconstruct the complete amplitude up to certain local terms, using the AdS version of dispersion relations
Summary
Focusing on the singularities of the one loop amplitudes, a time honored approach to study them uses unitarity which relates them to phase space integrals of products of lower-loop amplitudes. Note that being zeroth order in coupling constant, crefers to the OPE coefficients in the free theory, and c2 gives the conformal block coefficient for the disconnected diagrams. Similar formulae to those given above hold for the χχ → ψψ amplitude. This part of the amplitude is expressed exclusively in terms of the on-shell data for tree-level amplitudes and in this respect is analogous to the singular part of flat space amplitudes computed using unitarity.. With new features and subtleties that arise in the case of HSGRA taken into account, the formula (2.5) will be the starting point for our calculation of the singular part of the one-loop amplitude arising from the double cut
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