String theory and the classical stability of plane waves

Abstract

The presence of fields with negative mass-squared typically leads to some form of instability in standard field theories. The observation that, at least in the light-cone gauge, strings propagating in plane wave spacetimes can have worldsheet scalars with such tachyon-like masses suggests that the supergravity background may itself be unstable. To address this issue, we perform a perturbative analysis around the type IIB vacuum plane wave, the solution which most obviously generates worldsheet scalars with negative mass-squared. We argue that this background is perturbatively stable.

On zero-point energy, stability and Hagedorn behavior of type-IIB strings on pp-waves

“…The backgrounds we are considering preserve 16 supersymmetries and thus one would be tempted to conclude that they have to be stable. But, as observed in [10], due to the fact that pp-wave backgrounds are not asymptotically flat, we cannot trivially extend here the standard arguments relating supersymmetry and stability. In flat space the light-cone energy gives the space-time mass spectrum for the string states and a negative value signals the presence of a 10-D tachyon (see for example the Type 0 case).…”

“…with all a i being real, and so we can avoid worldsheet "tachyons" in light-cone gauge. This is the case we will consider here, taking in mind that a more general solution can involve negative squared mass, and referring to [10,12] for an analysis of this case. Thus, the only problem we face here is the negativity of E 0 .…”

“…This in turn implies the presence of negative mass squared worldsheet fields, and rises the question of stability in a natural way. Nevertheless, in [10,12] it was argued that those backgrounds are classically stable. In our case, with a five-form turned on, we can solve the supergravity e.o.m.…”

“…This was adopted in a pp-wave context by [10,12] to study the stability of plane-wave backgrounds with no flux turned on; these are potentially problematic because the supergravity e.o.m. require 8 i=1 a 2 i = 0, which means that some of the a i has to be imaginary.…”

Homogeneous plane waves

“…From the usual arguments [2] (see also [37,38]) one sees that these metrics are singular at x + = 0 and geodesically incomplete because geodesics starting off at some finite x + will reach the singularity at x + = 0 in finite proper time.…”