Perturbative Gauge Theory and Closed String Tachyons

TL;DR

This paper uncovers a direct link between instabilities in non-supersymmetric large N gauge theories and tachyonic modes in the twisted sectors of orbifold string theories, revealing a gauge/string correspondence.

Contribution

It establishes a precise correspondence between gauge theory double-trace coupling flows and string theory tachyonic instabilities in orbifold backgrounds.

Findings

Tachyonic twisted sectors correspond to gauge theory instabilities.

Stable sectors have double-trace couplings flowing to fixed points.

One-to-one mapping between gauge theory stability and string tachyons.

Abstract

We find an interesting connection between perturbative large N gauge theory and closed superstrings. The gauge theory in question is found on N D3-branes placed at the tip of the cone R^6/Gamma. In our previous work we showed that, when the orbifold group Gamma breaks all supersymmetry, then typically the gauge theory is not conformal because of double-trace couplings whose one-loop beta functions do not possess real zeros. In this paper we observe a precise correspondence between the instabilities caused by the flow of these double-trace couplings and the presence of tachyons in the twisted sectors of type IIB theory on orbifolds R^{3,1}x R^6/Gamma. For each twisted sectors that does not contain tachyons, we show that the corresponding double-trace coupling flows to a fixed point and does not cause an instability. However, whenever a twisted sector is tachyonic, we find that the corresponding one-loop beta function does not have a real zero, hence an instability is likely to exist in the gauge theory. We demonstrate explicitly the one-to-one correspondence between the regions of stability/instability in the space of charges under Gamma that arise in the perturbative gauge theory and in the free string theory. Possible implications of this remarkably simple gauge/string correspondence are discussed.