Hidden finite symmetries in string theory and duality of dualities

Abstract

Different compactifications of six-dimensional string theory on M 4 × 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.