GJMS-like operators on symmetric 2-tensors and their gravitational duals

TL;DR

This paper explores higher-derivative conformal operators on symmetric 2-tensors in Einstein spaces, their holographic duals involving massive gravitons, and provides formulas for their quantum determinants, confirming results in specific dimensions.

Contribution

It introduces a holographic framework for higher-derivative conformal operators on tensors and relates their determinants to massive graviton spectra in AdS/CFT.

Findings

Holographic duals involve bulk massive gravitons.

Derived formulas for functional determinants of higher-derivative operators.

Confirmed consistency with known results in 4 and 6 dimensions.

Abstract

We study a family of higher-derivative conformal operators $P_{2k}^{(2)}$ acting on transverse-traceless symmetric 2-tensors on generic Einstein spaces. They are a natural generalization of the well-known construction for scalars. We first provide the alternative description in terms of a bulk Poincar\'e-Einstein metric by making use of the AdS/CFT dictionary and argue that their holographic dual generically consists of bulk massive gravitons. At one-loop quantum level, we put forward a holographic formula for the functional determinant of the higher-derivative conformal operators $P_{2k}^{(2)}$ in terms of the functional determinant for massive gravitons with standard and alternate boundary conditions. The analogous construction for vectors $P_{2k}^{(1)}$ is worked out as well and we also rewrite the holographic formula for unconstrained vector and traceless symmetric 2-tensor by decoupling the longitudinal part. Finally, we show that the holographic formula provides the necessary building blocks to address the massless and partially massless bulk gravitons. This is confirmed in four and six dimensions, verifying full agreement with results available in the literature.