nLab C-field gauge algebra -- references

Supergravity $C$-Field gauge algebra

Identifying the super-graded gauge algebra of the C-field in D=11 supergravity (with non-trivial super Lie bracket $[v_3, v_3] = -v_6$):

• Eugene Cremmer, Bernard Julia, H. Lu, Christopher Pope; Equation (2.6) of: Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities, Nucl. Phys. B 535 (1998) 242-292 [doi:10.1016/S0550-3213(98)00552-5, arXiv:hep-th/9806106]

• I. V. Lavrinenko, H. Lu, Christopher N. Pope, Kellogg S. Stelle; (3.4) in: Superdualities, Brane Tensions and Massive IIA/IIB Duality, Nucl. Phys. B 555 (1999) 201-227 [doi:10.1016/S0550-3213(99)00307-7, arXiv:hep-th/9903057]

• Jussi Kalkkinen, Kellogg S. Stelle, (75) of: Large Gauge Transformations in M-theory, J. Geom. Phys. 48 (2003) 100-132 [doi:10.1016/S0393-0440(03)00027-5, arXiv:hep-th/0212081]

• Igor A. Bandos, Alexei J. Nurmagambetov, Dmitri P. Sorokin, (86) in: Various Faces of Type IIA Supergravity, Nucl.Phys. B 676 (2004) 189-228 [doi:10.1016/j.nuclphysb.2003.10.036, arXiv:hep-th/0307153]

• David Baraglia; §2.3 of: Leibniz algebroids, twistings and exceptional generalized geometry, Journal of Geometry and Physics 62 5 (2012) 903–934 [doi:10.1016/j.geomphys.2012.01.007, arXiv:1101.0856 math.DG]

  (in the context of Bn-geometry)

See also:

• André Coimbra, Charles Strickland-Constable, Daniel Waldram; (2.12) in: Supergravity as Generalised Geometry II: $E_{d(d)} \times \mathbb{R}^+$ and M theory [doi:10.1007/JHEP03(2014)019, arXiv:1212.1586 hep-th]

• J. A. Rosabal: Holographic partition function of democratic M-theory, JHEP (2026) [arXiv:2512.21741 hep-th]

Identification as an $L_\infty$-algebra (a dg-Lie algebra, in this case):

• Hisham Sati, (4.9) in: Geometric and topological structures related to M-branes, in Superstrings, Geometry, Topology, and $C^\ast$-algebras, Proc. Symp. Pure Math. 81 (2010) 181-236 [ams:pspum/081, arXiv:1001.5020 math.DG]

and identificatoin with the rational Whitehead $L_\infty$-algebra (the rational Quillen model) of the 4-sphere (cf. Hypothesis H):

• Hisham Sati, Alexander Voronov, (13) in: Mysterious Triality and M-Theory [arXiv:2212.13968]

• Hisham Sati, Urs Schreiber, (22) in: Flux Quantization on Phase Space [arXiv:2312.12517]