Flow of Geometries and Instantons on the Null Orbifold

TL;DR

The paper investigates time-dependent null orbifold singularities in string theory, employing D(-1) instanton probes and twisted-sector condensation to understand possible resolutions. It establishes a concrete link between the null orbifold and the well-understood $Z_N$ orbifolds by showing that closed-string twisted condensation drives an IR flow toward a boosted $\text{Z}_N$ geometry in the Higgs branch, with an intermediate relation to $\mathbb{R}\times\mathbb{C}/\mathbb{Z}_N$. Using first-quantized string analysis and a D(-1) instanton matrix model, the authors map out the Higgs and Coulomb branches and derive an IR effective action that matches between the null and boosted $Z_N$ descriptions, up to normalization. The results hint that the null singularity could be smoothed by twisted-sector effects and motivate further exploration of connections to BTZ microstates and higher-order corrections, though some IR sectors (notably the Y/Coulomb sectors) require additional work.

Abstract

We study condensation of twisted sector states in the null orbifold geometry. As the singularity is time-dependent, we probe it using D-Instantons. We present evidence that the null-orbifold flows to the $Z_N$ orbifold. We also comment on the subtleties of quantizing the closed superstring in this background.