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Minimal surfaces in \(q\)-deformed \(\mathrm{AdS}_{5}\times \mathrm{S}^{5}\) with Poincaré coordinates. (English) Zbl 1318.81040

Summary: We study minimal surfaces in \(q\)-deformed \(\mathrm{AdS}_{5}\times \mathrm{S}^{5}\) with a new coordinate system introduced in the previous work [the authors, ibid. 48, No. 7, Article ID 075401, 37 p. (2015; Zbl 1326.81159)]. In this paper, we introduce Poincaré coordinates for the deformed theory. We then 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. This finiteness indicates that the \(q\)-deformation may be regarded as a UV regularization.

MSC:

81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T08 Constructive quantum field theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations

Citations:

Zbl 1326.81159
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