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arXiv · 2502.20822

Solitonic vortices and black holes with vortex hair in AdS$_3$

Roberto Auzzi·Stefano Bolognesi·Giuseppe Nardelli·Gianni Tallarita·Nicolò Zenoni
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Abstract

We study soliton and black hole solutions with scalar hair in AdS$_3$ in a theory with a Maxwell field and a charged scalar field with double trace boundary conditions, which can trigger the dual boundary theory to become a superconductor. We investigate the phase diagram as a function of the temperature $T$ and of the double trace coupling $\kappa$ and we find a rich pattern of phase transitions, which can be of the Hawking-Page kind or can be due to the condensation of the order parameter. We also find a transition between vortex solutions and the zero temperature limit of the black hole for a critical value of the double trace coupling $\kappa$. The Little-Park periodicity is realized for the dual of the black hole solution with hair as a shift in the winding number and in the gauge field.

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Roberto Auzzi, Stefano Bolognesi, Giuseppe Nardelli, Gianni Tallarita, Nicolò Zenoni. 2025-02-28. Solitonic vortices and black holes with vortex hair in AdS$_3$. https://arxiv.org/abs/2502.20822

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