Talk:N = 4 supersymmetric Yang–Mills theory

In the article the Lagrangian is given as: $L=tr\left\{{\frac {1}{2g^{2}}}F_{\mu \nu }F^{\mu \nu }+{\frac {\theta _{I}}{8\pi ^{2}}}F_{\mu \nu }{\bar {F}}^{\mu \nu }-i\gamma ^{a}\sigma ^{\mu }D_{\mu }\lambda _{a}-D_{\mu }X^{i}D^{\mu }X^{i}+gC_{i}^{ab}\lambda _{a}[X^{i},\lambda _{b}]+C_{iab}\lambda ^{a}[X^{i},\lambda ^{b}]+{\frac {g^{2}}{2}}[X^{i},X^{j}]^{2}\right\}$

But in the reference the Lagrangian reads: $L=tr\left\{-{\frac {1}{2g^{2}}}F_{\mu \nu }F^{\mu \nu }+{\frac {\theta _{I}}{8\pi ^{2}}}F_{\mu \nu }{\tilde {F}}^{\mu \nu }-i{\bar {\lambda }}^{a}{\bar {\sigma }}^{\mu }D_{\mu }\lambda _{a}-D_{\mu }X^{i}D^{\mu }X^{i}+gC_{i}^{ab}\lambda _{a}[X^{i},\lambda _{b}]+{\bar {C}}_{iab}{\bar {\lambda }}^{a}[X^{i},{\bar {\lambda }}^{b}]+{\frac {g^{2}}{2}}[X^{i},X^{j}]^{2}\right\}$

I am not an expert on this topic, maybe the two formulations are equivalent or the source is wrong.

Randrian (talk) 08:02, 14 September 2012 (UTC)

Good spot. The minus sign was missing. Proving the importance of references! — Preceding unsigned comment added by 86.156.93.90 (talk) 19:28, 16 September 2012 (UTC)

Basic Question

The title of this article is N = 4 supersymmetric Yang–Mills theory. What is confusing to me, is whether there is a difference between a "supersymmetric" theory and a basic N=4 Yang-Mills theory. If all N=4 Yang-Mills models support SUSY interpretation, then can we rename the article as N = 4 Yang–Mills theory, and explain in the article that it must contain SUSY? We could create redirects from the current title, even. If there is a difference, I feel the article shous spend more time explaining the SUSY aspect of the distinction. 70.247.175.236 (talk) 18:19, 2 January 2014 (UTC)

It is a sort of redundant name, but that is what it is called. Plus it emphasizes how super this theory is (good or bad thing depending on your goal). AHusain (talk) 05:44, 4 January 2014 (UTC)

There is more than one supersymmetric Yang–Mills theory, not only N=4 supersymmetry. There is also N=1 supersymmetry and N=2 supersymmetry, and in other numbers of spacetime dimensions there may be others. I'm not sure what you mean by "all N=4 Yang-Mills models support SUSY interpretation", as the "N=4" part basically says how much supersymmetry you have. MuDavid (talk) 02:01, 26 August 2015 (UTC)

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