arXiv 1803.047482018-03hep-th

有限耦合下平面$AdS_4/CFT_3$的光谱研究

Exploring the spectrum of planar $AdS_4/CFT_3$ at finite coupling

Diego Bombardelli, Andrea Cavaglià, Riccardo Conti, Roberto Tateo

备注：: 42 pages, 11 figures, Mathematica notebooks and data files containing numerical results are attached; v2: published version
DOI：: 10.1007/JHEP04(2018)117

摘要：

在$\mathfrak{sl}(2|1)$扇区内的态的耦合常数为有限值时，数值求解了平面$\mathcal{N}=6$超共形Chern-Simons（SCS）的量子谱曲线（QSC）方程.通过调整最近提出的QSC微扰解的算法，获得了$\mathfrak{sl}(2)$类扇区外算子共形维数的新的弱耦合结果。除了有趣的是在自己的权利，这些微扰的结果是必要的初始输入的数值算法收敛到正确的解决方案。非微扰的数值结果很好地插值于弱耦合和已知的半经典展开式之间，并从数值结果中推导出新的强耦合精确结果。最后，我们的分析排除了算子$\textbf{20}$的TBA方程中的轮廓交叉奇点的存在。本文的结果是对该模型的QSC形式主义的一个重要检验，为新的定量研究开辟了道路，并为支持$AdS_4 \times CP^3$上的$\mathcal{N}=6$ SCS和IIA型超弦理论之间的强/弱耦合对偶性提供了进一步的证据。随附于arXiv提交文件中，提供了数值方法的Mathematica实现和包含数值结果的辅助文件。

英文摘要：

The Quantum Spectral Curve (QSC) equations for planar $\mathcal{N}=6$ super-conformal Chern-Simons (SCS) are solved numerically at finite values of the coupling constant for states in the $\mathfrak{sl}(2|1)$ sector. New weak coupling results for conformal dimensions of operators outside the $\mathfrak{sl}(2)$-like sector are obtained by adapting a recently proposed algorithm for the QSC perturbative solution. Besides being interesting in their own right, these perturbative results are necessary initial inputs for the numerical algorithm to converge on the correct solution. The non-perturbative numerical outcomes nicely interpolate between the weak coupling and the known semiclassical expansions, and novel strong coupling exact results are deduced from the numerics. Finally, the existence of contour crossing singularities in the TBA equations for the operator $\textbf{20}$ is ruled out by our analysis. The results of this paper are an important test of the QSC formalism for this model, open the way to new quantitative studies and provide further evidence in favour of the conjectured weak/strong coupling duality between $\mathcal{N}=6$ SCS and type IIA superstring theory on $AdS_4 \times CP^3$. Attached to the arXiv submission, a Mathematica implementation of the numerical method and ancillary files containing the numerical results are provided.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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