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.
Highlights
The emergence of gauge/gravity duality in the past decade has been instrumental in our understanding of strongly correlated systems
We start by writing down the metric for a static black hole in AdS3þ1 spacetime with Eddington-Finkelstein coordinates [24], ds2 1⁄4 l2 1⁄2−fðuÞdt2 − 2dtdu þ dr2 þ r2dθ2; ð1Þ u2 where the blackening factor is given by fðuÞ 1⁄4 ð1 − u3Þ: Here, l is the anti–de Sitter (AdS) radius, and u is the bulk direction scaled in such a way that u 1⁄4 0 is the AdS boundary and u 1⁄4 1 is the event horizon of the black hole
We have holographically devised vortex solutions with different winding numbers in a rotating superfluid. These solutions may be interpreted as vortices placed at the center of the disk at r 1⁄4 0
Summary
The emergence of gauge/gravity duality in the past decade has been instrumental in our understanding of strongly correlated systems. Numerical studies leading to the existence of such vortices in a rotating holographic superfluid have been carried out in [24,25]. We have analyzed this model very near to the critical value of rotation Ωc, where superfluid vortex state appears. To solve the holographic system in the bulk direction, we have used a variational technique known as Stürm-Liouville eigenvalue approach From this analysis, we observe that the chemical potential must be purely imaginary in order to get a consistent solution. In order to understand imaginary chemical potential in this holographic model, we have further solved the timedependent equations for the matter field. We conclude that an increase in the imaginary chemical potential leads to decrease in vortex number, which implies less dissipation in the system. V of this paper, we have concluded and made some remarks on our results
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