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arXiv 1405.2687hep-th
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$AdS_3$中具有混合3-形式通量的自旋弦和极小曲面

Spinning strings and minimal surfaces in $AdS_3$ with mixed 3-form fluxes

Justin R. David, Abhishake Sadhukhan

备注：
34 pages, Accepted for publication in JHEP
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摘要：

受最近提出的混合三种形式流的$AdS_3\times S^3$中S矩阵的启发，我们研究了具有Ramond和Neveu-Schwarz三种形式流的$AdS_3$中的经典折叠弦自旋.我们求解了这些弦的运动方程，得到了它们的色散与Neveu-Schwarz通量$b$中首阶的关系。我们表明，色散关系的自旋弦与大自旋${\cal S}$获得一项由$-\frac{\sqrtλ}{2π} b^2\log^2 {\cal S}$除了通常的$\frac{\sqrtλ}π \log {\cal S}$长期$\sqrtλ$是成比例的$AdS_3$的半径的平方。利用SO（2，2）变换和再参数化，我们证明了这些自旋弦可以与具有Neveu-Schwarz通量$b$的$AdS_3$中的类Wilson光圈有关.我们观察到，在类光威尔逊环的区域中的对数发散也被自旋弦色散关系中的$ b^2 \log^2 {\cal S}$项的相同系数所变形。这一结果表明，$ b^2 \log^2 {\cal S}$的系数具有类似于$\log {\cal S}$项的系数的性质，称为尖点异常维数，并且可以使用最近提出的S-矩阵来确定耦合$λ$中的所有阶。

英文摘要：

Motivated by the recent proposal for the S-matrix in $AdS_3\times S^3$ 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 spinning strings with large spin ${\cal S}$ acquires a term given by $-\frac{\sqrtλ}{2π} b^2\log^2 {\cal S}$ in addition to the usual $\frac{\sqrtλ}π \log {\cal S}$ term where $\sqrtλ$ 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 \log^2 {\cal S}$ term in the dispersion relation of the spinning string. This result indicates that the coefficient of $ b^2 \log^2 {\cal S}$ has a property similar to the coefficient of the $\log {\cal S}$ 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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