Exact WKB methods in SU(2) Nf = 1
Exact WKB methods in SU(2) Nf = 1
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DOI：
10.1007/jhep01(2022)046
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发表时间：
2021-05
影响因子：
5.4
通讯作者：
A. Grassi;Qianyu Hao;Andrew Neitzke
中科院分区：
文献类型：
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作者：
A. Grassi;Qianyu Hao;Andrew Neitzke
本文详细研究了四维SU（2）= 2单味SQCD理论对应的薛定谔方程。我们计算的Voros符号，或量子周期，在四个不同的方式：Borel求和的WKB系列，直接计算的Wronskians指数衰减的解决方案，TBA方程的Gaiotto-Moore-Neitzke/Gaiotto，和瞬子计数。我们用所有这些方法进行计算，发现很好的一致性。我们还研究了精确的量子化条件的频谱，我们计算Fredholm行列式的逆薛定谔算子使用TS/ST对应和Zamolodchikov的TBA，再次找到良好的协议。此外，我们还从两个方面探讨了Borel变换WKB级数的奇异性与BPS态之间的关系：4d理论的BPS态与量子周期的Borel变换WKB级数的奇异性有关; 2d+ 4d耦合系统的BPS态与薛定谔方程局部解的Borel变换WKB级数的奇异性有关。
We study in detail the Schrödinger equation corresponding to the four dimensional SU (2)= 2 SQCD theory with one flavour. We calculate the Voros symbols, or quantum periods, in four different ways: Borel summation of the WKB series, direct computation of Wronskians of exponentially decaying solutions, the TBA equations of Gaiotto-Moore-Neitzke/Gaiotto, and instanton counting. We make computations by all of these methods, finding good agreement. We also study the exact quantization condition for the spectrum, and we compute the Fredholm determinant of the inverse of the Schrödinger operator using the TS/ST correspondence and Zamolodchikov’s TBA, again finding good agreement. In addition, we explore two aspects of the relationship between singularities of the Borel transformed WKB series and BPS states: BPS states of the 4d theory are related to singularities in the Borel transformed WKB series for the quantum periods, and BPS states of a coupled 2d+ 4d system are related to singularities in the Borel transformed WKB series for local solutions of the Schrödinger equation.