Tachyon Stabilization in the AdS/CFT Correspondence

TL;DR

This paper explores the stability of tachyons in the AdS/CFT correspondence, linking gauge theory singularities to string theory instabilities and suggesting stability can be achieved by adjusting the AdS radius.

Contribution

It proposes a gauge theory perspective on tachyon instability in AdS/CFT, relating it to operator dimension singularities and large N graph summation effects.

Findings

Tachyon instability correlates with singularities in operator dimensions.

Stability can be restored by reducing the AdS radius below a critical value.

Large N planar graph summation influences the stability regime.

Abstract

We consider duality between type 0B string theory on $AdS_5\times S^5$ and the planar CFT on $N$ electric D3-branes coincident with $N$ magnetic D3-branes. It has been argued that this theory is stable up to a critical value of the `t Hooft coupling but is unstable beyond that point. We suggest that from the gauge theory point of view the development of instability is associated with singularity in the dimension of the operator corresponding to the tachyon field via the AdS/CFT map. Such singularities are common in large $N$ theories because summation over planar graphs typically has a finite radius of convergence. Hence we expect transitions between stability and instability for string theories in AdS backgrounds that are dual to certain large $N$ gauge theories: if there are tachyons for large AdS radius then they may be stabilized by reducing the radius below a critical value of order the string scale.