Central charges $C_J$ and $C_T$ in QED${}_d$-GNY model and scalar QED${}_d$

We compute the leading-order $1\mathrm{/}N$ corrections to the central charges $C_J$ and $C_T$ in the conformal QED${}_d$-Gross-Neveu-Yukawa (GNY) model and the scalar QED${}_d$ in $d$ dimensions. The scaling dimensions of the lowest adjoint bilinear scalars are obtained to order $O(1\mathrm{/}N)$ for general $d$. In $d=3$, the $U(1)$ Abelian gauge theory possesses a topological $U(1)$ global symmetry, and we evaluate the central charge $C_J^{\text{top}}$ of the topological symmetry current to subleading order in the $1\mathrm{/}N$ expansion. Our interest in these theories is primarily motivated by their potential connection to the $SO(5)$ symmetric deconfined quantum critical point (DQCP). We compare the large $N$ results for the central charges $C_J$ and $C_T$ with the conformal data of the $SO(5)$ DQCP obtained from fuzzy sphere and conformal bootstrap. The large $N$ predictions of the QED${}_3$-GNY model are found to be in reasonable agreement with the nonperturbative estimates for the $SO(5)$ DQCP.