Open-Closed-Open Triality Beyond Matrix Models

TL;DR

This paper investigates open-closed-open triality in twisted holography, demonstrating how open string descriptions relate to emergent bulk spacetime and matching probe brane actions to giant gravitons.

Contribution

It introduces a new perspective on triality in twisted holography, connecting open string field theories, matrix models, and geometric backreaction in a unified framework.

Findings

Two equivalent open string descriptions are derived from brane configurations.

Effective potentials from open strings capture backreaction on geometry.

Probe brane actions match those of giant gravitons in the deformed conifold.

Abstract

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.