Minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with Poincare coordinates

Abstract

We study minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with a new coordinate system introduced in the previous work 1408.2189. In this letter, we introduce Poincare coordinates for the deformed theory. Then we construct minimal surfaces whose boundary shape is a circle. The solution corresponds to a 1/2 BPS circular Wilson loop in the $q\to 1$ limit. A remarkable point is that the classical Euclidean action is not divergent unlike the original one. This finiteness indicates that the $q$-deformation may be regarded as a UV regularization.

arXiv comment22 pages, 1 figure, LaTeX, typos corrected, further clarifications

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• Comments on 2D dilaton gravity system with a hyperbolic dilaton potential
• Deformations of the Almheiri-Polchinski model
• Spiky strings in $\varkappa$-deformed $AdS$
• D-brane on Deformed AdS_3 times S^3
• Lax pairs on Yang-Baxter deformed backgrounds
• Yang-Baxter deformations and string dualities