Open-Closed-Open Triality Beyond Matrix Models

We explore the ideas of open-closed-open triality within twisted holography. Starting from two transverse stacks of branes in the B-model on the resolved conifold, we obtain two equivalent open string descriptions. Both are full-fledged field theories. In the appropriate limit, they simplify to gauged $\beta\gamma$-systems with determinant insertions, as expected from open string field theory. The $\rho$-matrix models that have appeared previously in the literature appear from an on-shell analysis of the field-theory actions. Most importantly, we show that the effective potential generated by integrating out the open strings on the other stack of branes exactly captures their backreaction on the geometry. In particular, we match the action of the probe branes to that of giant gravitons in the $\textit{deformed}$ conifold. The second open string description of the triality thus directly diagnoses the emergent bulk spacetime.