Charged Strings and Spectrum-Generating Algebra

We consider a system that both ends of a charged open string are attached on the D$p$-brane with constant electromagnetic fields. Contrary to neutral strings, the quantization of charged strings has not been so far considered well. For this system we construct the spectrum-generating algebra (SGA), which involves the cyclotron frequency. When the cyclotron frequency is set to be zero, the SGA is reduced to the ordinary SGA for neutral strings. The new SGA for charged strings guarantees that this system is ghost-free if certain conditions are satisfied. We also consider its application to the Hall effect for charged strings.