Theory HEP Seminar

Boundary Terms and Three-Point Functions: An AdS/CFT Puzzle Resolved

Dan Freedman

MIT/Stanford

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 Δ=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 AdS₄ boundary requires a finite A³ counterterm that does provide a perfect match to the field theory correlator. Bulk scalars with Δ=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.