Large N gauge theories and the Weak Gravity Conjecture
We classify large N limit of four-dimensional supersymmetric gauge theories with simple gauge groups that are flowing to superconformal fixed points. We restrict ourselves to the ones without superpotential and with a fixed flavor symmetry. We find that many of the examples exhibiting free energy grows linearly in N, instead of N^2 as expected from the matrix degrees of freedom of gauge theory. We also find that the ones with linear growth of free energy possess a dense spectrum of gauge-invariant operators forming a band of low conformal dimensions. We find that the AdS version of the Weak Gravity Conjecture (WGC) holds for all the cases in our category even though many examples do not have weakly-coupled holographic duals in AdS. This implies that the WGC goes beyond the Einstein-like semi-classical gravity.