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Factorization algebra

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arxiv 2310.06137 v2 pith:O5ABIWW7 submitted 2023-10-09 math-ph math.MP

classification math-phmath.MP
keywords algebrasexamplesfactorizationtheoryencompassesfieldlikephysics
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Factorization algebras are local-to-global objects living on manifolds, and they arise naturally in mathematics and physics. Their local structure encompasses examples like associative algebras and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In the setting of quantum field theory, factorization algebras articulate a minimal set of axioms satisfied by the observables of a theory, and they capture concepts like the operator product and correlation functions. In this survey article for the Encyclopedia of Mathematical Physics, 2nd Edition, we give the definitions and key examples, compare this approach with other approaches to mathematically formalizing field theory, describe key results, and explain how higher symmetries can be encoded in this framework.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On coefficients of operator product expansions for quantum field theories with ordinary, holomorphic, and topological spacetime dimensions

    hep-th 2025-02 conditional novelty 5.0 of 10

    For theories with mixed topological, holomorphic, and ordinary spacetime dimensions, OPE coefficients are proposed to be sheaf cohomology classes, with singular derived coefficients appearing under explicit dimension-...

  2. Celestial Chiral Algebras and Self-Dual Gravity

    hep-th 2025-07 conditional novelty 4.0 of 10

    This thesis derives deformations of celestial chiral algebras in self-dual gravity on curved backgrounds, obtaining W(infinity) on Eguchi-Hanson space, Ldiff_q(C) under Moyal deformation, and a two-parameter deformati...

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