ScalingStacks

Remark 4.10 . [0476]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Remark 4.10.

The positive and the negative vertices have drastically different features at refined scales: for example the positive vertex contains a fully nonlinear region modelled on the Taub-NUT type metric on ℂ3\mathbb{C}^{3}, while the negative vertex metric is obtained by a perturbative analysis. Nonetheless they share the same renormalisation flow equation, which controls large scale behaviours. The insight is that mirror symmetry should govern metric behaviours at large scales, but not necessarily at refined scales. In this perspective mirror symmetry owes its predicative power to the fact that questions in algebraic or symplectic geometry are mostly insensitive to small scale metric fluctuations.

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.