Novel vortices and the role of complex chemical potential in a rotating holographic superfluid

TL;DR

This paper analytically constructs novel vortex solutions in a rotating holographic superfluid, revealing that the chemical potential must be purely imaginary and linking vortex properties to the imaginary chemical potential.

Contribution

It introduces new vortex solutions in a rotating holographic superfluid and uncovers the necessity of an imaginary chemical potential for these solutions.

Findings

Vortex solutions are eigenfunctions of angular momentum.

Higher winding vortices correspond to higher quantized rotation.

Imaginary chemical potential reduces vortex winding number and dissipation.

Abstract

In this work, we have analytically devised novel vortex solutions in a rotating holographic superfluid. To achieve this result, we have considered a static disc at the AdS boundary and let the superfluid rotate relative to it. This idea has been numerically exploited in [1] where formation of vortices in such a setting was reported. We have found that these vortex solutions are eigenfunctions of angular momentum. We have also shown that vortices with higher winding numbers are associated with higher quantized rotation of the superfluid. We have, then, analysed the equation of motion along bulk AdS direction using St\"urm-Liouville eigenvalue approach. A surprising outcome of our study is that the chemical potential must be purely imaginary. We have then observed that the winding number of the vortices decreases with the increase in the imaginary chemical potential. We conclude from this that imaginary chemical potential leads to less dissipation in such holographic superfluids.