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On pq-duality and explicit solutions in $c \le 1$ $2d$ gravity models
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abstract
We study the integral representation for the exact solution to nonperturbative $c le 1$ string theory. A generic solution is determined by two functions $W(x)$ and $Q(x)$ which behaive at infinity like $x^p$ and $x^q$ respectively. The integral model for arbitrary $(p,q)$ models is derived which explicitely demonstrates $p-q$ duality of minimal models coupled to gravity. We discuss also the exact solutions to string equation and reduction condition and present several explicit examples.
Forward citations
Cited by 2 Pith papers
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An explicit four-corner dictionary for (2,p) minimal Liouville gravity
For the Lee-Yang series of minimal Liouville gravity, the four Frobenius and spectral-curve descriptions agree at genus zero after one per-insertion factor, and the resonance map is a tree-level Kontsevich frame change.
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$x-y$ swap for $(2,2p+1)$ minimal string
An x-y swapped spectral curve is conjectured to reproduce (2,2p+1) minimal string tachyon correlators without resonance transformations; verified at low genus, with a ground-ring extension that does not match HEM.
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