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Eleven-dimensional supergravity as a Calabi–Yau twofold

  • Fabian Hahner [1] ; Ingmar Saber [2]
    1. [1] Heidelberg University

      Heidelberg University

      Stadtkreis Heidelberg, Alemania

    2. [2] Ludwig Maximilian University of Munich

      Ludwig Maximilian University of Munich

      Kreisfreie Stadt München, Alemania

  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 2, 2025
  • Idioma: inglés
  • DOI: 10.1007/s00029-025-01024-x
  • Enlaces
  • Resumen

    • We construct a generalization of Poisson–Chern–Simons theory, defined on any supermanifold equipped with an appropriate filtration of the tangent bundle. Our construction recovers interacting eleven-dimensional supergravity in Cederwall’s formulation, as well as all possible twists of the theory, and does so in a uniform and geometric fashion. Among other things, this proves that Costello’s description of the maximal twist is the twist of eleven-dimensional supergravity in its pure spinor description. It also provides a pure spinor lift of the interactions in the minimally twisted theory. Our techniques enhance the BV formulation of the interactions of each theory to a homotopy Poisson structure by defining a compatible graded-commutative product; this suggests interpretations in terms of deformations of geometric structures on superspace, and provides some concrete evidence for a first-quantized origin of the theories.

  • Referencias bibliográficas
    • Alekseevsky, D.V., David, L.: Prolongation of Tanaka structures: an alternative approach. Ann. Mat. Pura Appl. 196, 1137–1164 (2017)
    • Alekseevsky, D.V., David, L.: Tanaka structures (non-holonomic G-structures) and Cartan connections. J. Geom. Phys. 91, 88–100 (2015)
    • Avramov, L., Golod, E.: Homology algebra of the Koszul complex of a local Gorenstein ring. Math. Notes Acad. Sci. USSR 9, 30–32 (1971)
    • Bashkirov, D., Voronov, A.A.: The BV formalism for L∞-algebras. J. Homot. Relat. Struct. 12, 305– 327 (2016)
    • Berkovits, N.: Towards covariant quantization of the supermembrane. J. High Energy Phys. 2002, 051–051 (2002)
    • Berkovits, N., Nekrasov, N.: The character of pure spinors. Lett. Math. Phys. 74, 75–109 (2005). arXiv:hep-th/0503075
    • Bershadsky, M., Cecotti, S., Ooguri, H., Vafa, C.: Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes. Comm....
    • Brown, R.: The twisted Eilenberg–Zilber theorem. Celebrazioni Arch. Secolo XX, Simp. Top (1967), pp 34–37
    • Cap, A., Slovák, J.: Parabolic geometries I. Mathematical Surveys and Monographs 154. American Mathematical Society (2009)
    • Cederwall, M.: D = 11 supergravity with manifest supersymmetry. Mod. Phys. Lett. A 25, 3201–3212 (2010)
    • Cederwall, M.: Towards a manifestly supersymmetric action for eleven-dimensional supergravity. JHEP 01, 117 (2010)
    • Cederwall, M.: Pure spinor superfields – an overview. Springer Proc. Phys. (Ed.) S. Bellucci, 153, pp 61–93 (2014). arXiv:1307.1762 [hep-th]
    • Cederwall, M.: SL(5) supersymmetry. Fortsch. Phys. 69(11–12), 2100116 (2021)
    • Cederwall, M., Jonsson, S., Palmkvist, J., Saberi, I.: Canonical supermultiplets and their Koszul duals (2023). arXiv:2304.01258 [hep-th]
    • Cederwall, M., Nilsson, B.E.W., Tsimpis, D.: Spinorial cohomology and maximally supersymmetric theories. JHEP 02, 009 (2002). arXiv:hep-th/0110069
    • Cirici, J., Wilson, S.O.: Dolbeault cohomology for almost complex manifolds. Adv. Math. 391, 107970 (2021)
    • Costello, K.: M-theory in the omega background and five-dimensional non-commutative gauge theory (2016). arXiv:1610.04144 [hep-th]
    • Costello, K., Gwilliam, O.: Factorization algebras in quantum field theory. Vol. 2. New Mathematical Monographs 41. Cambridge University Press...
    • Costello, K., Li, S.: Twisted supergravity and its quantization (2016). arXiv:1606.00365 [hep-th]
    • Cremmer, E., Julia, B., Scherk, J.: Supergravity theory in eleven dimensions. Phys. Lett. B 76, 409–412 (1978)
    • Del Zotto, M., Oh, J., Zhou, Y.: Evidence for an algebra of G2 instantons. JHEP 08, 214 (2022)
    • Deligne, P.: Théorie de Hodge: II. Publ. math. l’IHÉS 40, 5–57 (1971)
    • Dijkgraaf, R., Gukov, S., Neitzke, A., Vafa, C.: Topological M-theory as unification of form theories of gravity. Adv. Theor. Math. Phys....
    • Eager, R., Hahner, F.: Maximally twisted eleven-dimensional supergravity. Commun. Math. Phys. 398(1), 59–88 (2023)
    • Eager, R., Hahner, F., Saberi, I., Williams, B.R.: Perspectives on the pure spinor superfield formalism. J. Geom. Phys. 180, 104626 (2022)
    • Eager, R., Saberi, I., Walcher, J.: Nilpotence varieties. Ann. Henri Poincaré 22(4), 1319–1376 (2021)
    • Eisenbud, D.: Commutative algebra, with a view toward algebraic geometry. Graduate Texts in Mathematics 150. Springer-Verlag (1995)
    • Elliott, C., Hahner, F., Saberi, I.: The derived pure spinor formalism as an equivalence of categories. SIGMA 19, 022 (2023)
    • Friedan, D.: Notes on string theory and two-dimensional conformal field theory. Unified string theories 162 (1986)
    • Getzler, E.: Lie theory for nilpotent L∞ algebras. Ann. Math. 170(1), 271–301 (2009)
    • Golod, E.: On duality in the homology algebra of a Koszul complex. J. Math. Sci. 128, 3381–3383 (2005)
    • Hahner, F., Saberi, I.: To appear (2025)
    • Howe, P.S.: Pure spinors, function superspaces, and supergravity theories in ten and eleven dimensions. Phys. Lett. B 273(1–2), 90–94 (1991)
    • Kac, V.G.: Lie superalgebras. Adv. Math. 26(1), 8–96 (1977)
    • Kosmann-Schwarzbach, Y.: From Poisson algebras to Gerstenhaber algebras. Ann. l’Inst. Fourier 46(5), 1243–1274 (1996)
    • Koszul, J.-L.: Crochet de Schouten-Nijenhuis et cohomologie. fr. Astérisque S131 (1985). http://www. numdam.org/item/AST_1985_S131_257_0/
    • Lee, J.M.: Introduction to smooth manifolds. Graduate Texts in Mathematics 218. Springer-Verlag (2012)
    • Loday, J.-L., Vallette, B.: Algebraic operads. Grundlehren der mathematischen Wissenschaften 346. Springer-Verlag (2012)
    • Manin, Y.I.: New directions in geometry. Russ. Math. Surv. 39(6), 51 (1984)
    • Manin, Y.I.: Geometry of supergravity and Schubert supercells. J. Sov. Math. 31, 3362–3373 (1985)
    • Palmkvist, J.: The tensor hierarchy algebra. J. Math. Phys. 55, 011701 (2014)
    • Raghavendran, S., Saberi, I., Williams, B.R.: Twisted eleven-dimensional supergravity. Commun. Math. Phys. 402(2), 1103–1166 (2023). arXiv:2111.03049...
    • Raghavendran, S., Williams, B.R.: A holographic approach to the six-dimensional superconformal index (2022). arXiv:2210.07910 [math-ph]
    • Rosly, A.A., Schwarz, A.S., Voronov, A.A.: Geometry of superconformal manifolds. Commun. Math. Phys. 119, 129–152 (1988)
    • Roytenberg, D.: Courant algebroids, derived brackets, and even symplectic supermanifolds. University of California, Berkeley (1999)
    • Saberi, I., Williams, B.R.: Twisting pure spinor superfields, with applications to supergravity. Pure Appl. Math. Q. 20(2), 645–701 (2024)....
    • Saberi, I., Williams, B.R.: To appear (2025)
    • Tanaka, N.: On differential systems, graded Lie algebras, and pseudo-groups. J. Math. Kyoto Univ. 10(1), 1–82 (1970)
    • Vallette, B.: Algebra + homotopy = operad. Symplectic Poisson Noncommut. Geom. 62, 229–290 (2014)
    • Voronov, T.: Higher derived brackets and homotopy algebras. J. Pure Appl. Algebra 202(1–3), 133–153 (2005)
    • Williams, B.R., Elliott, C.: Holomorphic Poisson field theories. Higher Struct. 5, 1 (2021)
    • Witten, E.: String theory dynamics in various dimensions. Nucl. Phys. B 443, 85–126 (1995). arXiv:hep-th/9503124
    • Witten, E.: Notes on super Riemann surfaces and their moduli (2012). arXiv:1209.2459 [hep-th]
    • Zelenko, I.: On Tanaka’s prolongation procedure for filtered structures of constant type. SIGMA 5, 094 (2009)
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