nLab Hermann Nicolai

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Selected writings

Introducing what came to be called the Nicolai map:

• Hermann Nicolai, On a new characterization of scalar supersymmetric theories, Physics Letters B 89 3–4 (1980) Pages 341-346 [doi:10.1016/0370-2693(80)90138-0]

• Hermann Nicolai, Supersymmetry and functional integration measures, Nuclear Physics B

  176 2 (1980) 419-428 [doi:10.1016/0550-3213(80)90460-5]

• Hermann Nicolai, Supersymmetric functional integration measures, NATO Advanced Study Institute on Supersymmetry, Bonn (Aug 1984) 393-420 [cds:155731]

On the singleton representations of the orthosymplectic super Lie algebra:

• Hermann Nicolai, Ergin Sezgin, Singleton representations of $Osp(N,4)$, Physics Letters B, 143 4-6 (1984) 389-395

Realizing local $\mathfrak{su}(8)$ U-duality symmetry of D=11 supergravity:

• Bernard de Wit, Hermann Nicolai: D = 11 Supergravity With Local $SU(8)$ Invariance, Nucl. Phys. B 274, 363 (1986) [doi:10.1016/0550-3213(86)90290-7, spire:227409]

• Bernard de Wit, Hermann Nicolai: Local SU(8) invariance in $d = 11$ supergravity, talk at Nuffield Workshop on Supersymmetry and its Applications, 0357 [spire:218601]

Realizing local $\mathfrak{so}(18)$ U-duality symmetry of D=11 supergravity:

• Hermann Nicolai: $d=11$ Supergravity with local $SO(16)$ invariance, Physics Letters B 187 3–4 (1987) 316-320 [doi:10.1016/0370-2693(87)91102-6]

On D=2 supergravity:

• Hermann Nicolai: The integrability of $N=16$ supergravity, Physics Letters B 194 3 (1987) 402-407 [doi:10.1016/0370-2693(87)91072-0, spire:21766]

On quantization of the M2-brane Green-Schwarz sigma-model by the BFSS matrix model:

• Bernard de Wit, Jens Hoppe, Hermann Nicolai, On the Quantum Mechanics of Supermembranes, Nucl. Phys. B305 (1988) 545. (pdf, pdf, spire:261702)

• Bernard de Wit, W. Lüscher, Hermann Nicolai, The supermembrane is unstable, Nucl. Phys. B320 (1989) 135 (spire:266584, doi:10.1016/0550-3213(89)90214-9)

• Hermann Nicolai, Robert C. Helling, Supermembranes and M(atrix) Theory, In Trieste 1998, Nonperturbative aspects of strings, branes and supersymmetry 29-74 (arXiv:hep-th/9809103, spire:476366)

On gauged D=4 N=8 supergravity:

• Bernard de Wit, Hermann Nicolai, $N=8$ supergravity with local $SO(8)\times SU(8)$ invariance, Phys. Lett. 108 B (1982) 285 (doi:10.1016/0370-2693(82)91194-7)

• Bernard de Wit. Hermann Nicolai, $N = 8$ supergravity, Nucl. Phys. B208 (1982) 323 (doi:10.1016/0550-3213(82)90120-1)

On D=3 supergravity:

• Bernard de Wit, A. K. Tollsten, Hermann Nicolai, Locally supersymmetric D=3 non-linear sigma models, Nucl. Phys. B392 (1993) 3 (arXiv:hep-th/9208074)

On D=3 gauged supergravity and introducing the concept of embedding tensors:

• Hermann Nicolai, Henning Samtleben, Maximal gauged supergravity in three dimensions, Phys. Rev. Lett. 86 (2001) 1686-1689 (arXiv:hep-th/0010076)

• Hermann Nicolai, Henning Samtleben, Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions (arXiv:hep-th/0103032)

On U-duality symmetry of D=11 supergravity in view of M-theory:

• Hermann Nicolai: On M-Theory, J Astrophys Astron 20 (1999) 149–164 [arXiv:hep-th/9801090, doi:10.1007/BF02702349]

• Bernard de Wit, Hermann Nicolai: Hidden Symmetries, Central Charges and All That, Class. Quant. Grav. 18 (2001) 3095-3112 [arXiv:hep-th/0011239, doi:10.1088/0264-9381/18/16/302]

Discussion of E9 in view of U-duality-symmetry of D=11 supergravity reduced to $D=2$ (finite-dimensional representations of the maximal compact subalgebra $\mathfrak{k} = Lie\big(K(E_9)\big)$:

• Axel Kleinschmidt, Hermann Nicolai, Adriano Viganò: On spinorial representations of involutory subalgebras of Kac-Moody algebras, In: Partition Functions and Automorphic Forms, Moscow Lectures 5, Springer (2020) [arXiv:1811.11659, doi:10.1007/978-3-030-42400-8_4]

• Hermann Nicolai, Henning Samtleben: On $K(E_9)$, Pure and Applied Mathematics Quarterly 1 1 (2005) 180–204 [arXiv:hep-th/0407055, doi:10.4310/PAMQ.2005.v1.n1.a8]

• Axel Kleinschmidt, Ralf Köhl, Robin Lautenbacher, Hermann Nicolai: Representations of involutory subalgebras of affine Kac-Moody algebras, Commun. Math. Phys. 392 (2022) 89–123 [arXiv:2102.00870, doi:10.1007/s00220-022-04342-9]

On the maximal compact subalgebras of E9 and E10, respectively, and their finite-dimensional linear representations:

• Axel Kleinschmidt, Hermann Nicolai, Jakob Palmkvist: $K(E_9)$ from $K(E_{10})$, Journal of High Energy Physics 2007 JHEP06 (2007) [arXiv:hep-th/0611314, doi:10.1088/1126-6708/2007/06/051]

• Axel Kleinschmidt, Hermann Nicolai: On higher spin realizations of $K(E_{10})$, J. High Energ. Phys. 2013 41 (2013) [arXiv:1307.0413, doi:10.1007/JHEP08(2013)041]

• Axel Kleinschmidt, Hermann Nicolai: Generalised holonomies and $K(E_9)$, J. High Energ. Phys. 2021 54 (2021) [arXiv:2107.02445, doi:10.1007/JHEP09(2021)054]

On tensor hierarchies in gauged supergravity and possible relation to U-duality and M-theory:

• Bernard de Wit, Hermann Nicolai, Henning Samtleben, Gauged Supergravities, Tensor Hierarchies, and M-Theory, JHEP 0802:044, 2008 (arXiv:0801.1294)

On 4d gauged supergravity and 11d supergravity:

• Bernard de Wit, Hermann Nicolai, Deformations of gauged $SO(8)$ supergravity and supergravity in eleven dimensions (arXiv:1302.6219)

On U-duality in supergravity:

• Bernard de Wit, Hermann Nicolai, $D = 11$ Supergravity With Local $SU(8)$ Invariance, Nucl. Phys.

  B 274, 363 (1986)

• Hermann Nicolai, $D = 11$ Supergravity with Local $SO(16)$ Invariance , Phys. Lett. B 187, 316 (1987).

• K. Koepsell, Hermann Nicolai, Henning Samtleben, An exceptional geometry for $d = 11$ supergravity?, Class. Quant. Grav. 17, 3689 (2000) (arXiv:hep-th/0006034).

On a 1d sigma-model on a coset space of the E10 U-duality-group as a potential model for the M-theory-completion of 11D supergravity:

• Thibault Damour, Marc Henneaux, Hermann Nicolai: $E(10)$ and a “small tension expansion” of M theory, Phys. Rev. Lett. 89 221601 (2002) [arXiv:hep-th/0207267, doi:10.1103/PhysRevLett.89.221601]

• Thibault Damour, Hermann Nicolai: Eleven dimensional supergravity and the $E_{10}/K(E_{10})$ sigma-model at low $A_9$ levels, in Proceedings of the XXV International Colloquium on Group Theoretical Methods in Physics, 2-6 August 2004, Cocoyoc, Mexico, Routledge (2005) 93-111 [arXiv:hep-th/0410245, ISBN:9780750310086]

• Axel Kleinschmidt, Hermann Nicolai: $E(10)$ and $SO(9,9)$ invariant supergravity, JHEP 0407,

  041 (2004) [arXiv:hep-th/0407101, doi:10.1088/1126-6708/2004/07/041]

• Thibault Damour, Hermann Nicolai: Higher order M theory corrections and the Kac-Moody algebra $E_{10}$, Class. Quant. Grav. 22 (2005) 2849-2880 [arXiv:hep-th/0504153, doi:10.1088/0264-9381/22/14/003]

  (relating to higher curvature corrections)

• Axel Kleinschmidt, Hermann Nicolai: $E_{10}$ Cosmology, JHEP 01 (2006) 137 [arXiv:hep-th/0511290, doi:10.1088/1126-6708/2006/01/137]

  (cosmological solutions)

• Axel Kleinschmidt, Hermann Nicolai: Maximal supergravities and the $E_{10}$ model, International Journal of Modern Physics D 15 10 (2006) 1619-1642 [doi:10.1142/S0218271806009005]

• Thibault Damour, Axel Kleinschmidt, Hermann Nicolai: Constraints and the $E_{10}$ Coset Model, Class. Quant. Grav. 24 (2007) 6097-6120 [arXiv:0709.2691, doi:10.1088/0264-9381/24/23/025]

• Hermann Nicolai: Wonders of $E_{10}$ and $K(E_{10})$, talk at Wonders of Gauge Theory and Supergravity, IHP Paris (2008) [pdf]

• Eric A. Bergshoeff, Olaf Hohm, Axel Kleinschmidt, Hermann Nicolai, Teake A. Nutma, Jakob Palmkvist: $E_{10}$ and Gauged Maximal Supergravity, JHEP 0901:020 (2009) [doi:10.1088/1126-6708/2009/01/020, arXiv:0810.5767]

  (relation to D=3 gauged supergravity)

• Thibault Damour, Axel Kleinschmidt, Hermann Nicolai: Sugawara-type constraints in hyperbolic coset models, Commun. Math. Phys. 302 (2011) 755-788 [arXiv:0912.3491, doi:10.1007/s00220-011-1188-y]

• Hermann Nicolai, On Exceptional Geometry and Supergravity, talk at Gravitation, Solitons and Symmetries (2014) [pdf]

• Axel Kleinschmidt, Hermann Nicolai: The $E_{10}$ Wheeler-DeWitt operator at low levels, J. High Energ. Phys. 2022 92 (2022) [arXiv:2202.12676, doi:10.1007/JHEP04(2022)092]

  (relation to the Wheeler-DeWitt equation for 11D supergravity)

On E10 and E11 representation theory:

• Hermann Nicolai, Thomas Fischbacher: Low Level Representations for $E_{10}$ and $E_{11}$, in Kac-Moody Lie Algebras and Related Topics [arXiv:hep-th/0301017, doi:10.1090/conm/343]

On E10-U-duality exceptional field theory with fermions ($E_{10}/K(E_{10})$-coset model supersymmetric quantum mechanics):

• Axel Kleinschmidt, Hermann Nicolai: IIA and IIB spinors from $K(E_{10})$, Phys. Lett.B 637 (2006) 107-112 [arXiv:hep-th/0603205, doi:10.1016/j.physletb.2006.04.007]

• Thibault Damour, Axel Kleinschmidt, Hermann Nicolai: $K(E10)$, Supergravity and Fermions, JHEP 0608:046 (2006) [arXiv:hep-th/0606105, doi:10.1088/1126-6708/2006/08/046]

and speculation about relation to phenomenology (standard model of particle physics):

• Axel Kleinschmidt, Hermann Nicolai: Standard model fermions and $K(E_{10})$, Physics Letters B

  747 (2015) 251-254 [arXiv:1504.01586, doi:10.1016/j.physletb.2015.06.005]

On E9 BPS states:

• Francois Englert, Laurent Houart, Axel Kleinschmidt, Hermann Nicolai, Nassiba Tabti, An $E_9$ multiplet of BPS states, JHEP 0705:065 (2007) [arXiv:hep-th/0703285]

On infinite-dimensional Kac-Moody algebras as U-duality symmetries of D=11 supergravity, with focus on the example of E10:

• Hermann Nicolai (notes by Oliver Schlotterer): Infinite dimensional symmetries, lecture at Saalburg summer school in Wolfersdorf, Thuringia (2009) [pdf]

On super-heavy gravitinos as dark matter candidates, by embedding D=4 N=8 supergravity into E10-U-duality-invariant M-theory:

• Krzysztof A. Meissner, Hermann Nicolai, Standard Model Fermions and Infinite-Dimensional R-Symmetries, Phys. Rev. Lett. 121, 091601 (2018) (arXiv:1804.09606)

• Krzysztof A. Meissner, Hermann Nicolai, Planck Mass Charged Gravitino Dark Matter, Phys. Rev. D 100, 035001 (2019) (arXiv:1809.01441)

• Krzysztof A. Meissner, Hermann Nicolai, Supermassive gravitinos and giant primordial black holes (arXiv:2007.11889)

• Adrianna Kruk, Michał Lesiuk, Krzysztof A. Meissner, Hermann Nicolai: Signatures of supermassive charged gravitinos in liquid scintillator detectors [arXiv:2407.04883]

On higher spin gauge theory and Kac-Moody algebras:

• Marc Henneaux, Axel Kleinschmidt, Hermann Nicolai, Higher spin gauge fields and extended Kac-Moody symmetries (arXiv:1110.4460)

On a perturbation series for the M2-brane Green-Schwarz sigma-model quantized to the BFSS matrix model:

• Olaf Lechtenfeld, Hermann Nicolai, A perturbative expansion scheme for supermembrane and matrix theory (arXiv:2109.00346)

and on the relation to the string theory-dilaton under double dimensional reduction:

• Krzysztof A. Meissner, Hermann Nicolai, Fundamental Membranes and the String Dilaton [arXiv:2208.05822]

• Krzysztof A. Meissner, Hermann Nicolai, Evidence for a stable supermassive gravitino with charge $2/3$? [arXiv:2303.09131]

On quantum gravity:

• Hermann Nicolai, Quantum Gravity: the view from particle physics (arXiv:1301.5481)

On Lars Brink:

• Hermann Nicolai: Lars Brink 1943–2022, CernCourier (1 Mar 2023):

On the history of supersymmetry:

• Hermann Nicolai, Reflections on Supersymmetry [arXiv:2311.06051]

Survey of D=4 N=8 supergravity:

• Hermann Nicolai: $\mathcal{N}=8$ Supergravity, and beyond [arXiv:2409.18656]

Related entries

• Nicolai map

• supergravity, gauged supergravity

• M2-brane, BFSS matrix model

• E10, exceptional generalized geometry, U-duality

• dark matter

category: people