Bootstrapping Deconfined Quantum Tricriticality

The paradigmatic example of deconfined quantum criticality is the Neel to valence bond solid phase transition. The continuum description of this transition is the $N=2$ case of the $C{P}^{N-1}$ model, which is a field theory of $N$ complex scalars in 3D coupled to an Abelian gauge field with $\mathrm{S}\mathrm{U}(N)\times \mathrm{U}(1)$ global symmetry. Lattice studies and duality arguments suggest the global symmetry of the $C{P}^1$ model is enhanced to SO(5). We perform a conformal bootstrap study of SO(5) invariant fixed points with one relevant SO(5) singlet operator, which would correspond to two relevant $\mathrm{S}\mathrm{U}(2)\times \mathrm{U}(1)$ singlets, i.e., a tricritical point. We find that the bootstrap bounds are saturated by four different predictions from the large $N$ computation of monopole operator scaling dimensions, which were recently shown to be very accurate even for small $N$. This suggests that the Neel to valence bond solid phase transition is described by this bootstrap bound, which predicts that the second relevant singlet has dimension $\approx 2.36$.