On one loop corrections in higher spin gravity
Dmitry Ponomarev (Lebedev Institute of Physics, Leninsky ave. 53, Moscow, 119991, Russia, Texas A&M University, College Station, TX, 77843, U.S.A.); Ergin Sezgin (Texas A&M University, College Station, TX, 77843, U.S.A.); Evgeny Skvortsov (Lebedev Institute of Physics, Leninsky ave. 53, Moscow, 119991, Russia, Albert Einstein Institute, Am Muhlenberg 1, Potsdam-Golm, D-14476, Germany)
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.
