$x-y$ swap for $(2,2p+1)$ minimal string

TL;DR

This paper introduces an $x-y$ swap reformulation of the duality in $(2,2p+1)$ minimal string theory, simplifying the correspondence between worldsheet and matrix model correlators and enabling new amplitude computations.

Contribution

It proposes a new $x-y$ swap approach to minimal string duality, removing the need for resonance transformations and clarifying the duality's conceptual framework.

Findings

Reformulation of duality via $x-y$ swap in topological recursion

Elimination of resonance transformations in amplitude matching

Conjecture for computing non-tachyon operator amplitudes

Abstract

We continue the study of 2D gravity -- ``matrix model'' duality on the example of $(2,2p+1)$ minimal string. We propose a reformulation of the duality, related to a more conventional one by ``$x-y$ swap'' in the language of topological recursion. This formulation elucidates some conceptual and technical difficulties in the dictionary of the duality and relation to other examples. In particular, it allows to circumvent the necessity to use ``resonance transformations'', that were previously introduced to match the worldsheet and ``matrix model'' correlators, and the expressions for minimal string amplitudes in this approach are reminiscent of the ones obtained recently for ``complex Liouville string'' theory. Using this new approach, we also formulate a conjecture on how one can compute amplitudes with operators other than tachyons in the dual theory.