N=2 BPS谱的Galois覆盖与量子单值性
Galois covers of N=2 BPS spectra and quantum monodromy
摘要：
许多4d N=2理论的BPS谱可以看作是不同4d N=2模型的BPS谱的（范畴）伽罗瓦覆盖。伽罗瓦群G是覆盖N=2模型的物理对称。最简单的例子是N_f=2夸克的SU（2）SQCD，其BPS谱是纯SYM的BPS谱的Z_2覆盖。更一般地说，N= 2SYM具有单缀规范群，对所有k都有Z_k-覆盖，例如SO（8）SYM的Z_2-覆盖是SO（8）SYM耦合到E_6 Minahan-Nemeshanski SCFT的两个拷贝上。伽罗瓦盖大大简化了计算的BPS谱在G对称点，在有限和无限的腔室。当覆盖和商QFT允许几何工程时，例如对于S类模型，范畴谱覆盖可以实现为几何中的覆盖映射。一个特别好的例子是当谱伽罗瓦覆盖由主模曲线的模覆盖X（NM）-> X（M），或者更一般地，由正则格罗滕迪克的dessins d 'enfants诱导时;相应的N=2 QFT的BPS谱具有魔术性质。伽罗瓦覆盖允许有效地研究4d N=2 QFT的量子（半）单值性的作用。我们提出了几个例子和应用的光谱覆盖哲学。
英文摘要：
The BPS spectrum of many 4d N=2 theories may be seen as the (categorical) Galois cover of the BPS spectrum of a different 4d N=2 model. The Galois group G acts as a physical symmetry of the covering N=2 model. The simplest instance is SU(2) SQCD with N_f=2 quarks, whose BPS spectrum is a Z_2-cover of the BPS spectrum of pure SYM. More generally, N=2 SYM with simply--laced gauge group admits Z_k-covers for all k; e.g. the Z_2-cover of SO(8) SYM is SO(8) SYM coupled to two copies of the E_6 Minahan-Nemeshanski SCFT. Galois covers simplify considerably the computation of the BPS spectrum at G-symmetric points, in both finite and infinite chambers. When the covering and quotient QFTs admit a geometric engineering, say for class S models, the categorical spectral cover may be realized as a covering map in the geometry. A particularly nice instance is when the spectral Galois cover is induced by a modular cover of principal modular curves, X(NM)-> X(M), or, more generally, by regular Grothendieck's dessins d'enfants; the BPS spectra of the corresponding N=2 QFTs have magic properties. The Galois covers allow to study effectively the action of the quantum (half)monodromy of 4d N=2 QFTs. We present several examples and applications of the spectral covering philosophy.
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