Hidden Finite Symmetries in String Theory and Duality of Dualities

TL;DR

This paper uncovers hidden finite symmetries in string theory compactifications, revealing a discrete invariance group and its implications for dualities, scalar fields, and string solutions.

Contribution

It identifies a hidden discrete symmetry group in string compactifications and explores its role in dualities and the structure of scalar fields.

Findings

Discovery of a discrete invariance group in string compactification

Relation between scalar axidilaton and Kaluza-Klein vectors

Triadic correspondence among string types and pp wave solutions

Abstract

Different compactifications of six-dimensional string theory on $M_4 \times T^2$ are considered. Particular attention is given to the roles of the reduced modes as the $S$ and $T$ fields. It is shown that there is a discrete group of invariances of an equilateral triangle hidden in the model. This group is realized as the interchanges of the two-form fields present in the intermediate step of dimensional reduction in five dimensions. The key ingredient for the existence of this group is the presence of an additional $U(1)$ gauge field in five dimensions, arising as the dual of the Kalb-Ramond axion field strength. As a consequence, the theory contains more four-dimensional $SL(2,R)$ representations, with the resulting complex scalar axidilaton related to the components of the Kaluza-Klein vector fields of the naive dimensional reduction. An immediate byproduct of this relationship is a triadic correspondence among the fundamental string, the solitonic string, and a singular Brinkmann pp wave.