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

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.

D-branes in overcritical electric fields

“…It is also important to notice that a similar situation, in the presence of an electric background, would occur in superstring theory [4,9], whose spectrum does not originally contain a tachyon. The appearance of an infinite tower of tachyons has no analog in the absence (or in the presence of an undercritical) electric field.…”

“…The final stage representing the end of the rolling manifests itself in this toy model as a stable minimum of the reversed potential (corresponding to the old maximum) 9 .…”

“…where g, B are the sigma-model (closed string) constant backgrounds [8]. This, in turn, is the natural formula arising from the analysis of the conformal dimensions of the vertex operators of the worldsheet conformal field theory [8], and consistently from evaluation of the singularities of string scattering amplitudes (see [9] and references therein). For our purposes we will take the closed string metric to be g = η = (−1, 1, ..., 1).…”

“…We can now predict inside this toy model the value of the condensate for the infinite tachyonic tower. The final stage representing the end of the rolling manifests itself in this toy model as a stable minimum of the reversed potential (corresponding to the old maximum) 9 .…”

“…It is straightforward to check this at least numerically. 9 Of course it is open whether this feature is shared by the real String Field Theory potential. At this stage we take it as a conjecture.…”