Infrared behavior of Closed Superstrings in Strong Magnetic and Gravitational Fields

TL;DR

This paper analyzes the spectrum of four-dimensional supersymmetric closed superstrings under strong magnetic and gravitational fields, revealing stability limits, maximal magnetic field strength, and tachyonic instabilities.

Contribution

It derives the exact spectrum of superstring ground states with background fields and uncovers stability and instability regimes related to magnetic field strength.

Findings

Maximal magnetic field strength $H_{max} \,\sim\, M_{planck}^2$

States decouple at $H_{max}$ due to infinite mass

Tachyonic instabilities occur at strong fields but states stabilize again at higher fields

Abstract

A large class of four-dimensional supersymmetric ground states of closed superstrings with a non-zero mass gap are constructed. For such ground states we turn on 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 $H_{\rm max}\sim M_{\rm planck}^2$. 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 ${\cal O}(\mu M_{\rm planck})$ 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 ${\cal O}(M^2_{\rm planck})$. The implications of these results are discussed.