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arXiv 1204.4192hep-th
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弦与M理论的Ω变形

The Omega Deformation From String and M-Theory

Simeon Hellerman, Domenico Orlando, Susanne Reffert

摘要:

我们给出了Ω变形四维规范理论的弦论构造,其通值为ε_1和ε_2。我们的解决方案给出了显式描述的几何核心Nekrasov和Witten的实现的瞬子配分函数,远离渐近区域的背景。这个结构自然地提升到M-理论,并且对应于一个包裹在具有自对偶通量的黎曼曲面上的M5-膜。通过9-11翻转,我们终于重新解释欧米茄变形的非交换几何。我们的解产生了Ω-变形规范理论的所有修正耦合,也给出了相应的量子可积系统的量子谱曲线的几何原点。

英文摘要:

We present a string theory construction of Omega-deformed four-dimensional gauge theories with generic values of ε_1 and ε_2. Our solution gives an explicit description of the geometry in the core of Nekrasov and Witten's realization of the instanton partition function, far from the asymptotic region of their background. This construction lifts naturally to M-theory and corresponds to an M5-brane wrapped on a Riemann surface with a selfdual flux. Via a 9-11 flip, we finally reinterpret the Omega deformation in terms of non-commutative geometry. Our solution generates all modified couplings of the Ω-deformed gauge theory, and also yields a geometric origin for the quantum spectral curve of the associated quantum integrable system.

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