Generalizing Deconfined Criticality to 3D $N$-Flavor $\mathrm{SU}(2)$ Quantum Chromodynamics on the Fuzzy Sphere

The infra-red behaviour of gauge theories coupled to matter remains an open problem in quantum field theory. For a given gauge group, such theories are expected to flow to an interacting conformal fixed point over a range of fermion or scalar flavours, known as the `conformal window.' Their nature is important for understanding critical phases and phase transitions beyond the Landau paradigm like the deconfined quantum critical point (DQCP), yet remains challenging for conventional non-perturbative approaches. In this work, we study a family of fuzzy-sphere models corresponding to non-linear sigma models with $\mathrm{Sp}(N)$ global symmetry extended to the strongly-coupled region. These theories are expected have an infra-red fixed point described by $\mathrm{SU}(2)$ quantum chromodynamics (QCD) in three space-time dimensions with $N$ flavours of fermions. They can be viewed as a generalisation of the $\mathrm{SO}(5)$ DQCP, corresponding to $N=2$. We investigate them using quantum Monte Carlo for $N$ up to $16$. We find evidence that for $N\geq4$ the phase diagram contains a critical phase that appears to be absent for $N=2$. Within this phase, we measure the two-point correlation function and the excitation spectrum, which exhibit emergent conformal symmetry. We also extract the scaling dimension $\Delta_\phi$ of a leading operator and find consistency with large-$N$ expectations.