The AdS-CFT correspondence, consistent truncations and gauge invariance

TL;DR

This paper argues that for accurate AdS-CFT correlator calculations, one must use the full gauged supergravity action with nonlinear Kaluza-Klein ansatz, ensuring proper decoupling of massive modes and correct boundary correlators.

Contribution

It demonstrates that the full nonlinear KK ansatz is essential for correct correlator computation, extending previous linear approximations and analyzing gauge field and scalar truncations.

Findings

Full nonlinear KK ansatz reproduces consistent truncation to massless modes.

Using full gauged supergravity yields correct boundary correlators.

Linear ansatz only captures part of the gauged supergravity, leading to incomplete results.

Abstract

We give arguments for a conjecture made in a previous paper, that one has to use only the gauged sugra action for the calculation of correlators of certain operators via the AdS-CFT correspondence. The existence of consistent truncations implies that the massive modes decouple, and gauged supergravity is sufficient for computing n-point functions of CFT operators coupled to the massless (sugra) sector. The action obtained from the linear ansatz, of the type $\phi(x,y)=\phi_I(x)Y^I(y)$ gives only part of the gauged sugra. This means that there is a difference for the correlators on the boundary of AdS space. We find, studying examples of correlators, that the right prescription is to use the full gauged sugra, which implies using the full nonlinear KK ansatz. To this purpose, we analyze 3 point functions of various gauge fields in 5 and 7 dimensions, and the R-current anomaly in the corresponding CFT. We also show that the nonlinear rotation in the tower of scalar fields of Lee et al., Corrado et al. and Bastianelli and Zucchini produces a consistent truncation to the massless level and coincides with the Taylor expansion of the nonlinear KK ansatz in massless scalar fluctuations. Finally, we speculate about the way to do the full nonlinear rotation for the massive tower.