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Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory. (English) Zbl 1332.81197
Summary: We give an AdS/CFT interpretation to homogeneous Yang-Baxter deformations of the \(\mathrm{AdS}_5 \times \mathrm{S}^5\) superstring as noncommutative deformations of the dual gauge theory, going well beyond the canonical noncommutative case. These homogeneous Yang-Baxter deformations can be of so-called abelian or jordanian type. While abelian deformations have a clear interpretation in string theory and many already had well understood gauge theory duals, Jordanian deformations appear novel on both counts. We discuss the symmetry structure of the deformed string from the uniformizing perspective of Drinfeld twists and indicate that this structure can be realized on the gauge theory side by considering theories on various noncommutative spaces. We then conjecture that these are the gauge theory duals of our strings, modulo subtleties involving singularities. We support this conjecture by a brane construction for two jordanian examples, corresponding to noncommutative spaces with \([x^-\overset\star,x^i] \sim x^i\; (i = 1, 2)\). We also discuss \(\kappa\)-Minkowski type deformations of \(\mathrm{AdS}_5 \times \mathrm{S}^5\), one of which may be the gravity dual of gauge theory on spacelike \(\kappa\)-Minkowski space.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T20 Quantum field theory on curved space or space-time backgrounds
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T13 Yang-Mills and other gauge theories in quantum field theory
16T25 Yang-Baxter equations
11G09 Drinfel’d modules; higher-dimensional motives, etc.
14D15 Formal methods and deformations in algebraic geometry
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