Raviolo vertex algebras

• Niklas Garner ^[1] ; Brian R. Williams ^[2]
  1. [1] University of Oxford

     University of Oxford

     Oxford District, Reino Unido

     
  2. [2] Boston University

     Boston University

     City of Boston, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01042-9
• Enlaces
  • Texto completo
• Resumen

  • We develop an algebraic structure modeling local operators in a three-dimensional quantum field theory which is partially holomorphic and partially topological. The geometric space organizing our algebraic structure is called the raviolo (or bubble) and replaces the punctured disk underlying vertex algebras; we refer to this structure as a raviolo vertex algebra. The raviolo has appeared in many contexts related to three-dimensional supersymmetric gauge theory, especially in work on the affine Grassmannian. We prove a number of structure theorems for raviolo vertex algebras and provide simple examples that share many similarities with their vertex algebra counterparts.

• Referencias bibliográficas
  • Alfonsi, L., Kim, H., Young, C.A.S.: Raviolo vertex algebras, cochains and conformal blocks 1 (2024)
  • Arnold, V.I.: The cohomology ring of the group of dyed braids. Mat. Zametki 5, 227–231 (1969)
  • Asuke, T.: Godbillon–Vey Class of Transversely Holomorphic Foliations, MSJ Memoirs, vol. 24. Mathematical Society of Japan, Tokyo (2010)
  • Beem, C., Ben-Zvi, D., Bullimore, M., Dimofte, T., Neitzke, A.: Secondary products in supersymmetric field theory. Annales Henri Poincare...
  • Bezrukavnikov, R., Finkelberg, M., Mirkovi´c, I.: Equivariant homology and k-theory of affine grassmannians and toda lattices. Compos. Math....
  • Braverman, A., Finkelberg, M., Nakajima, H.: Towards a mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories,...
  • Bouaziz, E.: Tamarkin–Tsygan calculus and chiral Poisson cohomology. Nagoya Math. J. 248, 751–765 (2022)
  • Closset, C., Dumitrescu, T.T., Festuccia, G., Komargodski, Z.: Supersymmetric field theories on threemanifolds. JHEP 05, 017 (2013)
  • Closset, C., Dumitrescu, T.T., Festuccia, G., Komargodski, Z.: The geometry of supersymmetric partition functions. JHEP 01, 124 (2014)
  • Costello, K., Dimofte, T., Gaiotto, D.: Boundary chiral algebras and holomorphic twists. Commun. Math. Phys. 399(2), 1203–1290 (2023)
  • Costello, K., Gwilliam, O.: Factorization algebras in quantum field theory. Vol. 1, New Mathematical Monographs, vol. 31, Cambridge University...
  • Francesco, P,D., Mathieu, P., Sénéchal, D.: Conformal Field Theory, Graduate Texts in Contemporary Physics, Springer-Verlag, New York (1997)
  • Duchamp, T., Kalka, M.: Deformation theory for holomorphic foliations. J. Differ. Geom. 14(3), 317– 337 (1979)
  • Frenkel, E., Ben-Zvi, D.: Vertex algebras and algebraic curves, Mathematical Surverys and Monographs, vol. 88, American Mathematical Society...
  • Faonte, G., Hennion, B., Kapranov, M.: Higher Kac–Moody algebras and moduli spaces of G-bundles. Adv. Math. 346, 389–466 (2019)
  • Frenkel, E., Kac, V., Radul, A., Wang, W.-Q.: W1+∞ and W(glN ) with central charge N. Commun. Math. Phys. 170, 337–358 (1995)
  • Goddard, P.: Meromorphic conformal field theory, Infinite dimensional Lie algebras and groups: proceedings of the conference held at CIRM,...
  • Garner, N., Raghavendran, S., Williams, B.R.: Enhanced symmetries in minimally-twisted threedimensional supersymmetric theories 10 (2023)
  • Kac, V.: Vertex algebras for beginners, second edition, University Lecture Series, vol. 10, American Mathematical Society (1997)
  • Kamnitzer, J.: Symplectic resolutions, symplectic duality, and coulomb branches. Bull. Lond. Math. Soc. 54(5), 1515–1551 (2022)
  • Li, H.-S.: Local systems of vertex operators, vertex superalgebras and modules. J. Pure Appl. Algebra 109(2), 143–195 (1996)
  • Li, S.: Vertex algebras and quantum master equation. J. Differ. Geom. 123(3), 461–521 (2023)
  • Mason, G.: Vertex rings and their pierce bundles, pp. 45–104, American Mathematical Society, 01 (2018)
  • Nakajima, H.: Towards a mathematical definition of Coulomb branches of 3-dimensional N = 4 gauge theories, I. Adv. Theor. Math. Phys....
  • Oh, J., Yagi, J.: Poisson vertex algebras in supersymmetric field theories. Lett. Math. Phys. 110(8), 2245–2275 (2020)
  • Rawnsley, J.H.: Flat partial connections and holomorphic structures in C∞ vector bundles. Proc. Am. Math. Soc. 73(3), 391–397 (1979)
  • Tamarkin, D.: Deformations of chiral algebras. In: Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002),...
  • Totaro, B.: Configuration spaces of algebraic varieties. Topology 35(4), 1057–1067 (1996)
  • Zeng, K.: Monopole operators and bulk-boundary relation in holomorphic topological theories. SciPost Phys. 14(6), 153 (2023)