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Résumé |
This talk concerns an aspect of the AdS/CFT duality between the N=8 superconformal ABJM theory in d=3 and its gravity dual the
N=8, D=4 gauged supergravity. The CFT contains scalar operators O_i with conformal dimension Delta=1. Their 3-point correlation
function can be calculated non-perturbatively using supersymmetric localization and is non-vanishing. But the Lagrangian of the
gravity dual does not contain a bulk cubic coupling in the fields A_i dual to the O_i. So conventional Witten diagrams cannot furnish
the field theory result. We show that the extension of bulk supersymmetry to the AdS_4 boundary requires a finite A^3 counterterm
that does provide a perfect match to the field theory correlator. Bulk scalars with Delta=1 obey alternate quantisation, and the
generating function of their correlators is the Legendre transform of the on-shell action. The supersymmetry and dynamical
properties of the Legendre transform play an important role in our treatment.
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