ZZ Instantons and the Non-Perturbative Dual of c = 1 String Theory

Abstract

We study the effect of ZZ instantons in c = 1 string theory, and demonstrate that they give rise to non-perturbative corrections to scattering amplitudes that do not saturate unitarity within the closed string sector. Beyond the leading non-perturbative order, logarithmic divergences are canceled between worldsheet diagrams of different topologies, due to the Fischler-Susskind-Polchinski mechanism. We propose that the closed string vacuum in c = 1 string theory is non-perturbatively dual to a state of the matrix quantum mechanics in which all scattering states up to a given energy with no incoming flux from the "other side" of the potential are occupied by free fermions. Under such a proposal, we find detailed agreement of non-perturbative corrections to closed string amplitudes in the worldsheet description and in the dual matrix model.

arXiv comment28 pages, 10 figures; footnote and references added, typos corrected

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• The complex Liouville string: worldsheet boundaries and non-perturbative effects
• Nonperturbative definition of closed string theory via open string field theory
• String correlators on ${\text{AdS}}_3$: Four-point functions
• Asymptotically Free AdS3/CFT2
• Exact quantization and analytic continuation