Dipole binding in a cosmic string background due to quantum anomalies

We propose quantum dynamics for the dipole moving in cosmic string background and show that the classical scale symmetry of a particle moving in cosmic string background is still restored even in the presence of dipole moment of the particle. However, we show that the classical scale symmetry is broken due to inequivalent quantization of the nonrelativistic system. The consequence of this quantum anomaly is the formation of a bound state in the interval xi is an element of(-1,1). The inequivalent quantization is characterized by a one-parameter family of self-adjoint extension parameter Sigma. We show that within the interval xi is an element of(-1,1), a cosmic string with zero radius can bind the dipole and the dipole does not fall into the singularity.