On the breakdown of the perturbative interaction picture in Big Crunch/Big Bang or the true reason why perturbative string amplitudes on temporal orbifolds diverge

TL;DR

This paper explains why perturbative methods in string theory fail near space-like singularities, showing that the perturbative expansion breaks down while non-perturbative evolution remains well-defined.

Contribution

It reveals the fundamental breakdown of the perturbative interaction picture in backgrounds with space-like singularities, clarifying the divergence issues in string amplitudes on temporal orbifolds.

Findings

Perturbative S-matrix does not exist in certain singular backgrounds.

Non-perturbative evolution operator remains well-defined.

Perturbative string amplitudes diverge at the temporal orbifold singularity.

Abstract

We discuss how the perturbative particle paradigm fails in certain background with space-like singularity but asymptotically flat which should admit a S-matrix. The Feynman approach relies on the interaction picture. This approach means that we can interpret interactions as exchanges of particles. Particles are the modes of the quadratic part of the Lagrangian. In certain backgrounds with space-like singularity the interaction Hamiltonian is well defined but the perturbative expansion of the evolution operator through the singularity and the perturbative $S$ matrix do not exist. On the other hand, relying on minisuperspace approximation we argue that the non perturbative evolution operator does exist. The complete breakdown of the perturbative expansion explains why the perturbative computations in the covariant formalism in string theory in temporal orbifold fail, at least at the tree level.