The Dirichlet Obstruction in AdS/CFT

TL;DR

This paper investigates the Dirichlet obstruction in AdS/CFT, analyzing its structure across multiple dimensions and its connection to the conformal anomaly, with explicit calculations in specific dimensions.

Contribution

It provides a detailed computation of the Dirichlet obstruction in dimensions 6 to 10 and explores its relation to the conformal anomaly, advancing understanding of holographic reconstruction.

Findings

Computed Dirichlet obstruction in dimensions 6 to 10

Analyzed relationship between obstruction and conformal anomaly

Explicitly calculated conformal anomaly in dimension 8

Abstract

The obstruction for a perturbative reconstruction of the five-dimensional bulk metric starting from the four-dimensional metric at the boundary,that is, the Dirichlet problem, is computed in dimensions $6\leq d\leq 10$ and some comments are made on its general structure and, in particular, on its relationship with the conformal anomaly, which we compute in dimension $d=8$.