Bulk reconstruction for anti-symmetric and symmetric gauge fields: $p$-forms and the graviton

TL;DR

This paper develops explicit spacelike bulk reconstruction kernels for $p$-form fields and gravitons in AdS space, using mode-sum and Green's function methods, extending the HKLL procedure to these fields.

Contribution

It derives new spacelike bulk reconstruction kernels for $p$-forms and gravitons in AdS, including their covariant forms and alternative derivations, broadening the HKLL framework.

Findings

Derived spacelike kernels for $p$-forms and gravitons in AdS.

Presented mode-sum and Green's function derivations of the kernels.

Discussed massive $p$-forms and Breitenlohner-Freedman bounds.

Abstract

We consider the HKLL bulk reconstruction procedure for $p-$form fields and graviton in empty AdS$_{d + 1}$. We derive spacelike bulk reconstruction kernels for the $p$-forms and the graviton in the Poinarc\'e patch of AdS$_{d+1}$. The kernels are first derived via a mode-sum approach in arbitrary even dimensions. The appropriate AdS-covariant fields are identified and the corresponding kernels obtained via the mode sum approach for these fields. We present arguments for casting these kernels in terms of the AdS chordal distance. Introducing an antipodal-like mapping, the kernels are cast in a spacelike form. An alternative derivation is presented for these kernels, by using a chordal Green's function approach. From the asymptotic expansion of the bulk fields and using Green's theorem, we determine the spacelike kernels for both mode of $p-$forms and the graviton, which are show to agree with the kernels obtained by the mode-sum approach. The massive $p-$form fields, as well as the relevant Brietenlohner-Freedman bounds are also discussed.