ABJ Correlators with Weakly Broken Higher Spin Symmetry

摘要: We consider four-point functions of operators in the stress tensor multiplet 3d $\mathcal{N}=6$ $U(N)_k\times U(N+M)_{-k}$ or $SO(2)_{2k}\times USp(2+2M)_{-k}$ ABJ theories limit where $M$ and $k$ are taken to infinity while $N$ $\lambda\sim M/k$ held fixed. In this limit, these have weakly broken higher spin symmetry holographically dual gravity on $AdS_4$, $\lambda$ is bulk parity breaking parameter. use Ward identities, superconformal Lorentzian inversion formula fully determine tree level function up two free parameters. then supersymmetric localization fix both parameters for terms $\lambda$, so that our result correlator interpolates between theory at $\lambda=0$ a invariant interacting $\lambda=1/2$. compare CFT data extracted from recent numerical bootstrap conjecture exact spectrum $U(1)_{2M}\times U(1+M)_{-2M}$ (i.e. $\lambda=1/2$ $N=1$), find good agreement regime.