Instabilities in Strong Magnetic Fields in String Theory

TL;DR

This paper analyzes the spectrum and stability of string groundstates in strong magnetic fields, revealing a maximum magnetic field, decoupling of states, and conditions for tachyonic instabilities and stability.

Contribution

It provides an exact spectrum of string states in magnetic and curved backgrounds and identifies stability regimes and instabilities at high magnetic fields.

Findings

Existence of a maximal magnetic field $H_{max}$ beyond which states decouple.

Identification of tachyonic instabilities at certain strong background fields.

Discovery that states become stable again at magnetic fields near the Planck scale.

Abstract

We construct groundstates of the string with non-zero mass gap and non-trivial chromo-magnetic fields as well as curvature. The exact spectrum as function of the chromo-magnetic fields and curvature is derived. We examine the behavior of the spectrum, and find that there is a maximal value for the magnetic field $H_{\rm max}\sim M_{\rm Plank}^2$. At this value all states that couple to the magnetic field become infinitely massive and decouple. We also find tachyonic instabilities for strong background fields of the order ${\cal O}(\mu M_{\rm Plank})$ where $\mu$ is the mass gap of the theory. Unlike the field theory case, we find that such ground states become stable again for magnetic fields of the order ${\cal O}(M^2_{\rm Plank})$. The implications of these results are discussed.