One-loop unitarity of string theories in a constant external background and their Seiberg-Witten limit

TL;DR

This paper investigates one-loop open string amplitudes in a constant background B, revealing how the spectrum and poles are affected, and connects these findings to instabilities and tachyonic features in noncommutative field theories via the Seiberg-Witten limit.

Contribution

It provides a detailed analysis of one-loop open string spectra and factorization in a background B, highlighting new pole structures and their implications for noncommutative field theories.

Findings

Closed string spectrum remains unaffected by B.

Presence of double open-string poles due to symmetry loss.

Electric backgrounds induce classical instabilities and tachyonic cuts in noncommutative theories.

Abstract

Perturbative spectra and related factorization properties of one-loop open string amplitudes in the presence of a constant external background B are analysed in detail. While the pattern of the closed string spectrum, obtained after a careful study of the properly symmetrized amplitudes, turns out to be unaffected by the presence of B, a series of double open-string poles, which would be absent when B is turned off, can couple owing to a partial symmetry loss. These features are studied first in a bosonic setting and then generalized in the more satisfactory superstring context. When the background is of an ``electric'' type, a classical perturbative instability is produced beyond a critical value of the electric field. In the Seiberg-Witten limit this instability is the origin of the unphysical tachyonic cut occurring in the non-planar amplitudes of the corresponding noncommutative field theories.