Can free strings propagate across plane wave singularities?

Abstract

We study free string propagation in families of plane wave geometries developing strong scale-invariant singularities in certain limits. We relate the singular limit of the evolution for all excited string modes to that of the center-of-mass motion (the latter existing for discrete values of the overall plane wave profile normalization). Requiring that the entire excitation energy of the string should be finite turns out to be quite restrictive and essentially excludes consistent propagation across the singularity, unless dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).

Light-like big bang singularities in string and matrix theories

“…Because n 2 is finite, it is natural to expect that it does not affect the existence of the singular limit (governed by the singularity emerging from Ω(t/ǫ)). It can be proved that it is indeed the case for positive k [29].…”

“…We refer the reader to the original article [29] for detailed proofs, and here simply state the result: For k > 0, the singular limit of the excited mode evolution exists whenever it exists for the center-of-mass motion, and it is described by the following matching conditions:…”

“…However, this does not affect the result as long as one is only interested in the limiting expressions at ε = 0. More discussion is given in the original publication [29].…”

Aspects of plane wave (matrix) string dynamics

“…The (thus necessary) issue of regularisation of the particle and string dynamics in these singular backgrounds was taken up again in [25,26]. 3 In particular, in [26] a specific proposal was made to regularise the dynamics, namely by an explicit single-scale regularisation of the oscillator frequencies (equivalently, of the plane wave metric) of the form…”

“…in which the scale invariance of the original background is as much as possible respected. In [26,28] some minimal conditions were proposed for such a regularisation to lead to a well-defined quantum evolution in the limit ǫ → 0 that the regulator is removed. One of the purposes of this article is to analyse and scrutinise this proposal in some more detail.…”