Instantons and Conformal Holography

TL;DR

This paper explores the AdS_4/CFT_3 correspondence by explicitly matching bulk and boundary instanton solutions involving scalar fields, revealing insights into vacua and conformal symmetry breaking.

Contribution

It provides a detailed comparison of bulk and boundary instantons and identifies the dual boundary operator in the context of conformal holography.

Findings

Bulk and boundary instanton solutions are explicitly matched.

Quantum states in the bulk correspond to multiply-occupied boundary states.

The dual boundary operator to the bulk scalar is explicitly identified.

Abstract

We study a subsector of the AdS_4/CFT_3 correspondence where a class of solutions in the bulk and on the boundary can be explicitly compared. The bulk gravitational theory contains a conformally coupled scalar field with a Phi^4 potential, and is holographically related to a massless scalar with a Phi^6 interaction in three dimensions. We consider the scalar sector of the bulk theory and match bulk and boundary classical solutions of the equations of motion. Of particular interest is the matching of the bulk and the boundary instanton solutions which underlies the relationship between bulk and boundary vacua with broken conformal invariance. Using a form of radial quantization we show that quantum states in the bulk correspond to multiply-occupied single particle quantum states in the boundary theory. This allows us to explicitly identify the boundary composite operator which is dual to the bulk scalar, at the free theory level as well as in the instanton vacuum. We conclude with a discussion of possible implications of our results.