The perturbative c=1 string S-matrix equals a double-scaled matrix integral on the spectral curve x=2√2 cos(z), y=sin(z), establishing a worldsheet–MQM–matrix-integral triality.
Minimal String Theory
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abstract
We summarize recent progress in the understanding of minimal string theory, focusing on the worldsheet description of physical operators and D-branes. We review how a geometric interpretation of minimal string theory emerges naturally from the study of the D-branes. This simple geometric picture ties together many otherwise unrelated features of minimal string theory, and it leads directly to a worldsheet derivation of the dual matrix model.
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Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
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$c=1$ strings as a matrix integral
The perturbative c=1 string S-matrix equals a double-scaled matrix integral on the spectral curve x=2√2 cos(z), y=sin(z), establishing a worldsheet–MQM–matrix-integral triality.
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All the D-Branes of Resurgence
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.