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Seiberg–Witten Solution to Pure SU(2) Theory

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N=2 Supersymmetric Dynamics for Pedestrians

Part of the book series: Lecture Notes in Physics ((LNP,volume 890))

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Abstract

We are finally prepared enough to start the analysis of the simplest of non-Abelian \(\mathcal{N}=2\) supersymmetric theory, namely the pure SU(2) gauge theory. We mainly follow the presentation of the original paper [1], except that we use the Seiberg–Witten curve in the form first found in [2], which is more suited to the generalization later.

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Notes

  1. 1.

    Our usage of (z, x) for the coordinates follows the convention of [2]. Using (t, v) for what we call (z, x) is also common, which comes from [3].

  2. 2.

    It is real two-dimensional, and therefore it is a surface from a usual point of view. Mathematicians are strange and they consider one-dimensional objects curves, whether it is complex one-dimensional or real one-dimensional.

  3. 3.

    The symbol λ were for adjoint fermions up to this point, but we use λ mainly for the differential from now on, unless otherwise noted.

References

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Tachikawa, Y. (2015). Seiberg–Witten Solution to Pure SU(2) Theory. In: N=2 Supersymmetric Dynamics for Pedestrians. Lecture Notes in Physics, vol 890. Springer, Cham. https://doi.org/10.1007/978-3-319-08822-8_4

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