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Spinning strings and minimal surfaces in AdS 3 with mixed 3-form fluxes

A preprint version of the article is available at arXiv.

Abstract

Motivated by the recent proposal for the S-matrix in AdS 3 × S 3 with mixed three form fluxes, we study classical folded string spinning in AdS 3 with both Ramond and Neveu-Schwarz three form fluxes. We solve the equations of motion of these strings and obtain their dispersion relation to the leading order in the Neveu-Schwarz flux b. We show that dispersion relation for the spinnig strings with large spin \( \mathcal{S} \) acquires a term given by \( -\frac{\sqrt{\lambda }}{2\pi }{b}^2{ \log}^2\;\mathcal{S} \) in addition to the usual \( \frac{\sqrt{\lambda }}{\pi } \log\;\mathcal{S} \) term where \( \sqrt{\lambda } \) is proportional to the square of the radius of AdS 3. Using SO(2, 2) transformations and re-parmetrizations we show that these spinning strings can be related to light like Wilson loops in AdS 3 with Neveu-Schwarz flux b. We observe that the logarithmic divergence in the area of the light like Wilson loop is also deformed by precisely the same coefficient of the b 2 log2 \( \mathcal{S} \) term in the dispersion relation of the spinning string. This result indicates that the coefficient of b 2 log2 \( \mathcal{S} \) has a property similar to the coefficient of the log \( \mathcal{S} \) term, known as cusp-anomalous dimension, and can possibly be determined to all orders in the coupling λ using the recent proposal for the S-matrix.

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Correspondence to Abhishake Sadhukhan.

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ArXiv ePrint: 1405.2687

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David, J.R., Sadhukhan, A. Spinning strings and minimal surfaces in AdS 3 with mixed 3-form fluxes. J. High Energ. Phys. 2014, 49 (2014). https://doi.org/10.1007/JHEP10(2014)049

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Keywords

  • AdS-CFT Correspondence
  • Bosonic Strings
  • Long strings