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I have been working on Seiberg-Witten theory (well, I am now familiar with its computation), but i do not now the physical concept of this theory.

For example, i now from the duality of electro-magnetic field, the variable $(\begin{array}& a \\ a_D \end{array})$ and its relation comes out.

As far as I know, these variables are parameters of low effective action for $N=2$ IR action, $i.e$ parameters of pre-potential. $F$

And from the duality relation of $a$ and $a_D$ ($F$ and $F_D$) there are some relation like \begin{align} &\tau= \frac{\partial^2 F}{\partial a^2}, \quad \tau_D = \frac{\partial^2 F_D}{\partial a_D^2} \\ & a_D = \frac{\partial F}{\partial a}, \quad a = - \frac{\partial F_D}{\partial a_D} \end{align} and eventually obtain \begin{align} \tau_D = -\frac{1}{\tau} \end{align} which seemingly interested with dual gauge coupling and original coupling is kind of relation as strong-weak duality.

Take further, using the seiberg witten curve $\lambda$ \begin{align} a= \oint_{\gamma_1} \lambda, \quad a_D = \oint_{\gamma_2} \lambda \end{align} From this the mass spectrum of BPS particle \begin{align} M = n a + m a_D \end{align} which seemingly related with in $M$ theory picture's of n M2 brane and m M5 branes.


Can anyone make some comment of physical interpretation of $a, a_D, \tau, \tau_D$ or general comments of physical meaning of seiberg-witten theory? Any comment related with seiberg-witten theory is welcome!

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    $\begingroup$ Asking for "any comment on Seiberg-Witten theory" is a bit broad. Can you ask a more specific question? $\endgroup$ – ACuriousMind Aug 29 '15 at 19:51
  • $\begingroup$ @ACuriousMind, I mean its physical interpretation or physical application. $i.e$ role of brane picture, relation to topological string theory and so on. $\endgroup$ – phy_math Aug 30 '15 at 7:29
  • $\begingroup$ Same people always closing interesting questions, thank god an adult-level site exists for good questions like these... $\endgroup$ – bolbteppa Sep 23 '15 at 9:38