  QED with a large number $N$ of massless fermionic degrees of freedom has a
conformal phase in a range of space-time dimensions. We use a large $N$
diagrammatic approach to calculate the leading corrections to $C_T$, the
coefficient of the two-point function of the stress-energy tensor, and $C_J$,
the coefficient of the two-point function of the global symmetry current. We
present explicit formulae as a function of $d$ and check them versus the
expectations in 2 and $4-\epsilon$ dimensions. Using our results in higher even
dimensions we find a concise formula for $C_T$ of the conformal Maxwell theory
with higher derivative action $F_{\mu \nu} (-\nabla^2)^{\frac{d}{2}-2} F^{\mu
\nu}$. In $d=3$, QED has a topological symmetry current, and we calculate the
correction to its two-point function coefficient, $C^{\textrm{top}}_{J}$. We
also show that some RG flows involving QED in $d=3$ obey $C_T^{\rm UV} >
C_T^{\rm IR}$ and discuss possible implications of this inequality for the
symmetry breaking at small values of $N$.
