Argyres–Seiberg–Gaiotto Duality for $\mathop{\mathrm{SU}}(N)$ Theory

Abstract

We learned in the last chapter that the curve of $\mathop{\mathrm{SU}}(N)$ theory with 2N flavors is given by:

$$\displaystyle{ \frac{\prod _{i=1}^{N}(\tilde{x} -\tilde{\mu }_{i})} {\tilde{z}} + f\prod _{i=1}^{N}(\tilde{x} -\tilde{\mu }_{ i}^{{\prime}})\tilde{z} =\tilde{ x}^{N} +\tilde{ u}_{ 2}\tilde{x}^{N-2} + \cdots + u_{ N} }$$

(12.1.1)

where f is a complex number; the differential is $\tilde{\lambda }=\tilde{ x}\mathit{dz}/z$. This theory is superconformal, and f is a function of the UV coupling constant τ _UV . We would like to understand the strong-coupling limits of this theory.