CFT Description of Small Objects in AdS

TL;DR

This paper demonstrates that local operator expectation values in the CFT, via AdS/CFT, encode detailed information about small sources inside AdS, including their size and multipole moments, enabling differentiation between various compact objects.

Contribution

It shows that CFT expectation values contain comprehensive information about small sources in AdS, including size and multipole moments, which was not previously understood.

Findings

CFT expectation values encode multipole moments of sources.

Size of spherical sources can be determined from expectation values.

Expectation values can distinguish stars from black holes with the same mass.

Abstract

By the AdS/CFT correspondence, the expectation value of certain local operators in the CFT is given by the asymptotic value of supergravity fields. We show that these local expectation values contain a remarkable amount of information about small sources deep inside AdS_p x S^q. In particular, they contain essentially all the multipole moments. More importantly, one can use them to determine the size of a spherical source. This is not a small effect: The size appears in an exponentially large contribution to the expectation values. This provides an easy way for the CFT to distinguish stars from black holes with the same mass, or to distinguish different "giant graviton" configurations.