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Spinning strings in \(\mathrm{AdS}_4\times \mathbb{CP}^3\) and quantum corrections. (English) Zbl 1168.81379

Summary: We derive the one-loop correction to the space-time energy of a folded string in \(\text{AdS}_4\times \mathbb{CP}^{3}\) carrying spin S in \(\text{AdS}_4\) and angular momentum \(J\) in \(\mathbb{CP}^{3}\) in the long string approximation. From this general result in the limit \(J\ll \log S\) we obtain the one-loop correction to the cusp anomalous dimension which turns out to be \(\frac{-(5 \log 2)}{2\pi}\). This value appears to be in conflict with the prediction from the recently conjectured all-loop Bethe ansatz.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83E15 Kaluza-Klein and other higher-dimensional theories
83E30 String and superstring theories in gravitational theory
81T20 Quantum field theory on curved space or space-time backgrounds
81T13 Yang-Mills and other gauge theories in quantum field theory
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References:

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