Remarks on the critical dimension of left-handed string and its quasiconformal nature

TL;DR

This paper investigates the critical dimension of the chiral string, revealing that in the singular limit, it exhibits quasiconformal properties and a different central charge than the conventional string, challenging previous assumptions.

Contribution

It re-examines the critical dimension of the chiral string in a singular limit, showing it has quasiconformal mappings and a different central charge from the conventional string.

Findings

Central charge differs in the singular limit from the conventional string.

The worldsheet transformations are quasiconformal rather than conformal.

The critical dimension of the chiral string is re-evaluated in the singular limit.

Abstract

The chiral string without a singular gauge limit is argued to have the same critical dimension as its corresponding conventional closed string. Thus, its central charge would be the same as its conventional counterpart in the conformal gauge. Here, we would re-examine the critical dimension of the chiral string in the singular Hohm-Siegel-Zwiebach limit. A straight forward calculation of the operator product expansion (OPE) of the corresponding would-be stress tensor shows that the central charge term is not the same as its conventional counterpart when taking the singular limit. Instead of having a conformal transformation on the worldsheet, the coordinate reparametrization provides a set of quasiconformal mappings.