Strong Magnetic Limit of String Theory

TL;DR

This paper explores a specific magnetic limit in superstring theories where most string excitations become infinitely massive, leaving a simplified, supersymmetric 3+1 dimensional theory with unique thermodynamic properties.

Contribution

It introduces a novel magnetic limit in superstring theory that isolates a supersymmetric sector and analyzes its properties, including one-loop partition functions and spectrum reduction.

Findings

Most string excitations become infinitely massive in the limit.

The resulting theory is a 3+1 Lorentz invariant supersymmetric model.

No Hagedorn transition occurs at finite temperature in this limit.

Abstract

We show that there exists a certain limit in type I and type II superstring theory in the presence of a suitable configuration of magnetic U(1) fields where all string excitations get an infinite mass, except for the neutral massless sector and for the boson and fermion string states lying on the leading Regge trajectory. For a supersymmetric configuration of magnetic fields in internal directions, the resulting theory after the limit is a 3+1 Lorentz invariant supersymmetric theory. Supersymmetry can be broken by introducing extra components of the magnetic field or else by finite temperature. In both cases we compute the one-loop partition function for the type I string model after taking the limit, which turns out to be different from the Yang-Mills result that arises by a direct $\alpha'\to 0$ limit. In the case of finite temperature, no Hagedorn transition appears, in consistency with the reduction of the string spectrum. In type II superstring theory, the analogous limit is constructed by starting with a configuration of Melvin twists in two or more complex planes. The resulting theory contains gravitation plus an infinite number of states of the leading Regge trajectory.