Additional constraints for the tensor bootstrap

Abstract

Recently, new positivity constraints were suggested to constrain arbitrary unitary tensor integrals. In the present work, we explore two variants of these positivity constraints: one built from ``open bubbles'', which are tensor-like objects found by removing a tensor from a bubble invariant, and the second built from ``color matrices'', which are matrices found by removing a color contraction from a bubble invariant. Using these positivity constraints, we find sharp bounds on unitary tensor integrals at finite $N$, and probe deviations from Gaussian universality in this limit.