SL(2, Z) Multiplets of Type II Superstrings in $D < 10$

TL;DR

This paper constructs an infinite family of SL(2, Z) multiplet string solutions in type II superstring theories compactified to dimensions between 4 and 10, revealing new symmetry-related configurations.

Contribution

It introduces a novel set of string solutions permuted by SL(2, Z) symmetry in lower-dimensional superstring theories, extending known solutions from 10 dimensions.

Findings

Solutions characterized by two coprime integers as charges

Solutions are permuted by SL(2, Z) group

Brief discussion on stability and charge conservation

Abstract

It has been shown recently that the toroidally compactified type IIB string effective action possesses an SL(2, R) invariance. Using this symmetry we construct an infinite family of macroscopic string-like solutions permuted by SL(2, Z) group for type II superstrings in $4 \leq D < 10$. These solutions, which formally look very similar to the corresponding solutions in $D = 10$, are characterized by two relatively prime integers corresponding to the `electric' charges associated with the two antisymmetric tensor fields of the strings. Stability of these solutions is discussed briefly in the light of charge conservation and the tension gap equation.