Exact solutions to quantum spectral curves by topological string theory
Exact solutions to quantum spectral curves by topological string theory
复制标题
拓扑弦理论量子谱曲线的精确解
DOI：
10.1007/jhep10(2015)025
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发表时间：
2015
影响因子：
5.4
通讯作者：
J. Reuter
中科院分区：
文献类型：
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作者：
A. Klemm;M. Marino;J. Reuter
我们将量子谱问题与拓扑弦之间的猜想联系推广到许多具有任意质量参数的局部几乎del Pezzo曲面上。该猜想利用非精化和Nekrasov-Shatashvili极限中拓扑弦的微扰信息来非微扰地求解量子谱问题。我们考虑了三项算符O1，1，O1，2和O2，3的不同形变对应的局域几乎del Pezzo表面的量子谱曲线和E8 del Pezzo的质量形变。为了验证猜想，我们将对这些算符的谱的预测与对本征值的数值结果进行了比较。我们还从猜想的谱行列式中计算了前几个费米子谱迹，并将它们与谱理论中的解析和数值结果进行了比较。在所有这些比较中，我们发现该猜想得到了充分的验证，具有很高的数值精度。对于局域，我们将谱行列式展开到orbilold点附近，并发现了Jacobi theta函数之间有趣的关系。我们还给出了和的几何之间的显式映射以及从环面几何导出算子O，m，n的系统方法。
We generalize the conjectured connection between quantum spectral problems and topological strings to many local almost del Pezzo surfaces with arbitrary mass parameters. The conjecture uses perturbative information of the topological string in the unrefined and the Nekrasov-Shatashvili limit to solve non-perturbatively the quantum spectral problem. We consider the quantum spectral curves for the local almost del Pezzo surfaces ofand a mass deformation of the E 8 del Pezzo corresponding to different deformations of the three-term operators O 1, 1, O 1, 2 and O 2, 3. To check the conjecture, we compare the predictions for the spectrum of these operators with numerical results for the eigenvalues. We also compute the first few fermionic spectral traces from the conjectural spectral determinant, and we compare them to analytic and numerical results in spectral theory. In all these comparisons, we find that the conjecture is fully validated with high numerical precision. For localwe expand the spectral determinant around the orbifold point and find intriguing relations for Jacobi theta functions. We also give an explicit map between the geometries ofandas well as a systematic way to derive the operators O m, n from toric geometries.
影响因子：
1.9
作者：
A. Klemm;J. Manschot;Thomas Wotschke
通讯作者：
A. Klemm;J. Manschot;Thomas Wotschke
影响因子：
2.4
作者：
Jinwon Choi;S. Katz;A. Klemm
通讯作者：
Jinwon Choi;S. Katz;A. Klemm
DOI：
--
发表时间：
2010
期刊：
影响因子：
--
作者：
A. Kapustin;Brian Willett;Itamar Yaakov
通讯作者：
Itamar Yaakov