Quantum electrodynamics in 2+1 dimensions is an effective gauge theory for the so called algebraic quantum liquids. A new type of such a liquid, the algebraic charge liquid, has been proposed recently in the context of deconfined quantum critical points [R. K. Kaul {it et al.}, Nature Physics {bf 4}, 28 (2008)]. In this context, we show by using the renormalization group in $d=4-epsilon$ spacetime dimensions, that a deconfined quantum critical point occurs in a SU(2) system provided the number of Dirac fermion species $N_fgeq 4$. The calculations are done in a representation where the Dirac fermions are given by four-component spinors. The critical exponents are calculated for several values of $N_f$. In particular, for $N_f=4$ and $epsilon=1$ ($d=2+1$) the anomalous dimension of the Neel field is given by $eta_N=1/3$, with a correlation length exponent $ u=1/2$. These values change considerably for $N_f>4$. For instance, for $N_f=6$ we find $eta_Napprox 0.75191$ and $ uapprox 0.66009$. We also investigate the effect of chiral symmetry breaking and analyze the scaling behavior of the chiral holon susceptibility, $G_chi(x)equiv<bar psi(x)psi(x)bar psi(0)psi(0)>$.
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