Comment on Field Redefinitions in the AdS/CFT Correspondence

TL;DR

This paper demonstrates that field redefinitions in ten-dimensional Type IIB supergravity do not alter the holographic renormalization group structure or the Weyl anomaly in the AdS/CFT correspondence, confirming the invariance of physical quantities.

Contribution

It shows that specific field redefinitions in supergravity do not affect the holographic RG or anomalies, reinforcing the invariance of physical observables in AdS/CFT.

Findings

Field redefinitions do not change the holographic Weyl anomaly.

The holographic RG structure remains unaffected by metric redefinitions.

Supergravity's on-shell structure is invariant under these field redefinitions.

Abstract

We carry out field redefinitions in ten-dimensional Type IIB supergravity and show that they do not give rise to any physical corrections to the holographic renormalization group structure in the AdS/CFT correspondence. We in particular show that the holographic Weyl anomaly of the N=4 SU(N) super Yang-Mills theory does not change under the field redefinition of the ten-dimensional metric of the form G_{MN} -> G_{MN}+\alpha R G_{MN}+\beta R_{MN}. These results are consistent with the fact that classical supergravity represents the on-shell structure of massless modes of superstrings, which should not change under redefinitions of fields.