On-shell Action for Bubbling Geometries

TL;DR

This paper derives an on-shell action for half-BPS bubbling geometries in type IIB supergravity within the AdS/CFT framework, linking it to free fermion observables and suggesting a holographic surface in these geometries.

Contribution

It introduces an on-shell action for LLM bubbling solutions that connects supergravity to free fermion observables, advancing understanding of holography in these geometries.

Findings

On-shell action reproduces LLM solutions.

Duality with free fermion observables established.

Holographic surface in bubbling geometries suggested.

Abstract

We study the half-BPS sector of the AdS/CFT correspondence. In the full sector of the correspondence, on-shell actions in type IIB supergravity have been played crucial roles, for example in the GKP-Witten relation. We derive, therefore, an on-shell action that reproduces a class of half-BPS solutions found by Lin, Lunin and Maldacena. These solutions describe the bubbling geometries in the supergravity. We show that this on-shell action for the LLM solutions is dual to the classical limit of an observable of the N free fermions in a harmonic oscillator potential in 1+1 dimensions. The observable consists of three parts: an expectation value of the total energy, matrix elements of the momentum squared, and matrix elements of the position squared. Our results suggest that there exists a holographic correspondence on a two-dimensional surface in the bubbling geometries.