Bound States in the AdS/CFT Correspondence

TL;DR

This paper investigates how boundary terms in AdS scalar field theories influence the existence of bound states in the bulk, revealing that boundary conditions can induce or prevent such states beyond the Breitenlohner-Freedman bound.

Contribution

It explicitly computes boundary terms that determine bound state existence in AdS scalar theories, highlighting the role of boundary conditions beyond traditional stability bounds.

Findings

Bound states depend on boundary terms in the action.

Adding specific boundary terms can eliminate bound states.

The Breitenlohner-Freedman bound alone does not prevent bulk tachyons.

Abstract

We consider a massive scalar field theory in anti-de Sitter space, in both minimally and non-minimally coupled cases. We introduce a relevant double-trace perturbation at the boundary, by carefully identifying the correct source and generating functional for the corresponding conformal operator. We show that such relevant double-trace perturbation introduces changes in the coefficients in the boundary terms of the action, which in turn govern the existence of a bound state in the bulk. For instance, we show that the usual action, containing no additional boundary terms, gives rise to a bound state, which can be avoided only through the addition of a proper boundary term. Another notorious example is that of a conformally coupled scalar field, supplemented by a Gibbons-Hawking term, for which there is no associated bound state. In general, in both minimally and non-minimally coupled cases, we explicitly compute the boundary terms which give rise to a bound state, and which ones do not. In the non-minimally coupled case, and when the action is supplemented by a Gibbons-Hawking term, this also fixes allowed values of the coupling coefficient to the metric. We interpret our results as the fact that the requirement to satisfy the Breitenlohner-Freedman bound does not suffice to prevent tachyonic behavior from existing in the bulk, as it must be supplemented by additional conditions on the coefficients in the boundary terms of the action.