Supersymmetric Yang–Mills Theory (other)
Supersymmetric Yang–Mills may refer to * N = 1 supersymmetric Yang–Mills theory * Seiberg–Witten theory, corresponding to the low-energy action of N = 2 supersymmetric Yang–Mills theory * N = 4 supersymmetric Yang–Mills theory ''N'' = 4 supersymmetric Yang–Mills (SYM) theory is a relativistic conformally invariant Lagrangian gauge theory describing the interactions of fermions via gauge field exchanges. In ''D''=4 spacetime dimensions, ''N''=4 is the m ...

N = 1 Supersymmetric Yang–Mills Theory
In theoretical physics, more specifically in quantum field theory and supersymmetry, supersymmetric Yang–Mills, also known as super Yang–Mills and abbreviated to SYM, is a supersymmetric generalization of Yang–Mills theory, which is a gauge theory that plays an important part in the mathematical formulation of forces in particle physics. It is a special case of 4D N = 1 global supersymmetry. Super Yang–Mills was studied by Julius Wess and Bruno Zumino in which they demonstrated the supergauge-invariance of the theory and wrote down its action, alongside the action of the Wess–Zumino model, another early supersymmetric field theory. The treatment in this article largely follows that of Figueroa-O'Farrill's lectures on supersymmetry and of Tong. While N = 4 supersymmetric Yang–Mills theory is also a supersymmetric Yang–Mills theory, it has very different properties to \mathcal = 1 supersymmetric Yang–Mills theory, which is the theory discussed in this article. The \ ...
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Seiberg–Witten Theory
In theoretical physics, Seiberg–Witten theory is an \mathcal = 2 supersymmetric gauge theory with an exact low-energy effective action (for massless degrees of freedom), of which the kinetic part coincides with the Kähler potential of the moduli space of vacua. Before taking the low-energy effective action, the theory is known as \mathcal = 2 supersymmetric Yang–Mills theory, as the field content is a single \mathcal = 2 vector supermultiplet, analogous to the field content of Yang–Mills theory being a single vector gauge field (in particle theory language) or connection (in geometric language). The theory was studied in detail by Nathan Seiberg and Edward Witten . Seiberg–Witten curves In general, effective Lagrangians of supersymmetric gauge theories are largely determined by their holomorphic (really, meromorphic) properties and their behavior near the singularities. In gauge theory with \mathcal = 2 extended supersymmetry, the moduli space of vacua is a spe ...
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