{"paper":{"title":"Towards unified theory of $2d$ gravity","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A.Marshakov, A.Mironov, A.Morozov, A.Zabrodin, S.Kharchev","submitted_at":"1992-01-08T19:09:00Z","abstract_excerpt":"We introduce a new 1-matrix model with arbitrary potential and the matrix-valued background field. Its partition function is a $\\tau$-function of KP-hierarchy, subjected to a kind of ${\\cal L}_{-1}$-constraint. Moreover, partition function behaves smoothly in the limit of infinitely large matrices. If the potential is equal to $X^{K+1}$, this partition function becomes a $\\tau$-function of $K$-reduced KP-hierarchy, obeying a set of ${\\cal W} _K$-algebra constraints identical to those conjectured in \\cite{FKN91} for double-scaling continuum limit of $(K-1)$-matrix model. In the case of $K=2$ th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9201013","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"}