On the relevance of GIKS instability of charged N=4 SYM plasma

Recently Gladden, Ivo, Kovtun, and Starinets (GIKS) identified a novel instability of $\mathcal{N}=4$ supersymmetric Yang-Mills plasma with a diagonal $U(1)$ $R$-symmetry chemical potential. Since $\mathcal{N}=4$ SYM plasma has $R$-charged matter fields, it might suffer from the standard superconducting instability. We show that while the superconducting instability is indeed present, it happens at a lower critical temperature compare to that of the GIKS instability.