Neel-VBS transition in three-dimensional SU(N) antiferromagnets

We present results for the phase diagram of an SU(N) generalization of the Heisenberg antiferromagnet on a bipartite three-dimensional anisotropic cubic (tetragonal) lattice as a function of N and the lattice anisotropy gamma. In the "isotropic" gamma = 1 cubic limit, we find a transition from Neel to valence bond solid (VBS) between N = 9 and N = 10. We follow the Neel-VBS transition to the limiting cases of gamma << 1 (weakly coupled layers) and gamma >> 1 (weakly coupled chains). Throughout the phase diagram we find a direct first-order transition from Neel at small N to VBS at large N. In the three-dimensional models studied here, we find no evidence for either an intervening spin-liquid "photon" phase or a continuous transition, even close to the limit gamma << 1 where the isolated layers undergo continuous Neel-VBS transitions.