{"work":{"id":"dbf94bd9-1457-4c3c-be35-8ab4d42205cc","openalex_id":null,"doi":null,"arxiv_id":"hep-th/9206084","raw_key":null,"title":"Closed String Field Theory: Quantum Action and the BV Master Equation","authors":null,"authors_text":null,"year":1992,"venue":"hep-th","abstract":"The complete quantum theory of covariant closed strings is constructed in detail. The action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra $L_\\infty$, and the higher genus algebraic structure implies the Batalin-Vilkovisky (BV) master equation. From these structures on the off-shell state space, we show how to derive the $L_\\infty$ algebra, and the BV equation on physical states, recently constructed in d=2 string theory. The string diagrams are surfaces with minimal area metrics, foliated by closed geodesics of length $2\\pi$. These metrics generalize quadratic differentials in that foliation bands can cross. The string vertices are succinctly characterized; they include the surfaces whose foliation bands are all of height smaller than $2\\pi$.\n  --While this is not a review paper, an effort was made to give a fairly complete and accessible account of the quantum closed string field theory.--","external_url":"https://arxiv.org/abs/hep-th/9206084","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-07-04T15:39:56.680381+00:00","pith_arxiv_id":"hep-th/9206084","created_at":"2026-05-13T23:23:26.461514+00:00","updated_at":"2026-07-04T15:39:56.680381+00:00","title_quality_ok":true,"display_title":"Closed String Field Theory: Quantum Action and the BV Master Equation","render_title":"Closed String Field Theory: Quantum Action and the BV Master Equation"},"hub":{"state":{"tier_text":"hub","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":10,"external_cited_by_count":null},"tier":"hub","role_counts":[{"context_role":"background","n":3}],"polarity_counts":[{"context_polarity":"background","n":3}],"runs":{},"summary":{},"graph":{},"authors":[]}}