{"paper":{"title":"On pq-duality and explicit solutions in $c \\le 1$ $2d$ gravity models","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A.Marshakov, S.Kharchev","submitted_at":"1993-03-17T23:08:38Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9303100","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}