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Koszul duality in quantum field theory

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arxiv 2110.10257 v4 pith:WHOYWFWU submitted 2021-10-19 hep-th math-phmath.MP

classification hep-thmath-phmath.MP
keywords defectsdualitykoszulappearancearticleexampleslinesupersymmetric
verification ladder T0 review T1 audit T2 compute T3 formal
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In this article, we introduce basic aspects of the algebraic notion of Koszul duality for a physics audience. We then review its appearance in the physical problem of coupling QFTs to topological line defects, and illustrate the concept with some examples drawn from twists of various simple supersymmetric theories. Though much of the content of this article is well-known to experts, the presentation and examples have not, to our knowledge, appeared in the literature before. Our aim is to provide an elementary introduction for those interested in the appearance of Koszul duality in supersymmetric gauge theories with line defects and, ultimately, its generalizations to higher-dimensional defects and twisted holography.

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Cited by 3 Pith papers

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

  1. S-algebra in Gauge Theory: Twistor, Spacetime and Holographic Perspectives

    hep-th 2025-06 conditional novelty 7.0 of 10

    The celestial S-algebra is shown to unify the twistor, null-infinity, and twisted-holography descriptions of self-dual Yang-Mills, with new two-helicity charges and a nonlinear extrapolate dictionary.

  2. Twisting BFSS & IKKT

    hep-th 2026-02 conditional novelty 6.0 of 10

    The minimal supersymmetric twists of the IKKT and BFSS matrix models are computed in BV-BRST cohomology and matched, in the planar limit, to BCOV-type twisted IIB and IIA supergravity; the non-minimal twists are local...

  3. 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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