nLab self-duality for pregeometric RR-fields -- references

Discussion of (Lagrangian densities for) D=10 type II supergravity with “duality-symmetric”/“democratic”/“pregeometric” for of the RR-fields:

• Gianguido Dall'Agata, Kurt Lechner, Mario Tonin, $D=10$, $N=IIB$ Supergravity: Lorentz-invariant actions and duality, JHEP 9807:017 (1998) $[$arXiv:hep-th/9806140, doi:10.1088/1126-6708/1998/07/017$]$

• Eugene Cremmer, Bernard Julia, H. Lu, Christopher Pope, Section 3 of: Dualisation of Dualities, II: Twisted self-duality of doubled fields and superdualities, Nucl. Phys. B 535(1998) 242-292 $[$arXiv:hep-th/9806106, doi:10.1016/S0550-3213(98)00552-5$]$

• Eric Bergshoeff, Renata Kallosh, Tomas Ortin, Diederik Roest, Antoine Van Proeyen, New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls, Class. Quant. Grav. 18 (2001) 3359-3382 $[$arXiv:hep-th/0103233, doi:10.1088/0264-9381/18/17/303$]$

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

• Karapet Mkrtchyan, Fridrich Valach, Democratic actions for type II supergravities, Phys. Rev. D 107 6 (2023) 066027 [doi:10.1103/PhysRevD.107.066027, arXiv:2207.00626]

Enhancement of the self-duality constraint on pregeometric RR-fields from (twisted) de Rham cohomology to (twisted) topological K-theory (under the hypothesized K-theory classification of D-brane charge) in terms of a quadratic form on differential K-theory:

• Gregory Moore, Edward Witten, Self-Duality, Ramond-Ramond Fields, and K-Theory, JHEP 0005:032 (2000) $[$arXiv:hep-th/9912279$]$

• Edward Witten, Duality Relations Among Topological Effects In String Theory, JHEP 0005:031 (2000) $[$arXiv:hep-th/9912086, doi:10.1088/1126-6708/2000/05/032$]$

• Daniel Freed, Michael Hopkins, On Ramond-Ramond fields and K-theory, JHEP 0005 (2000) 044 $[$arXiv:hep-th/0002027$]$

• Daniel Freed, Dirac charge quantization and generalized differential cohomology, Surveys in Differential Geometry 7, Int. Press (2000) 129-194 $[$arXiv:hep-th/0011220, doi:10.4310/SDG.2002.v7.n1.a6, spire:537392$]$

An indication of a more refined discussion in twisted differential KR-theory:

• Jacques Distler, Dan Freed, Greg Moore, Orientifold Précis in: Hisham Sati, Urs Schreiber (eds.) Mathematical Foundations of Quantum Field and Perturbative String Theory, Proceedings of Symposia in Pure Mathematics, AMS (2011) $[$arXiv:0906.0795, slides$]$

See at orientifold for more on this.

Expressing the self-duality of pregeometric RR-fields in terms of 11d Chern-Simons theory:

• Dmitriy Belov, Greg Moore, Type II Actions from 11-Dimensional Chern-Simons Theories $[$arXiv:hep-th/0611020$]$

Some review:

• Richard Szabo, section 3.6 and 4.6 of: Quantization of Higher Abelian Gauge Theory in Generalized Differential Cohomology, ESI 2385 (2012) $[$arXiv:1209.2530, pdf$]$

Discussion in the context of flux quantization (here: D-brane charge quantization in K-theory):

• SS23, §3.3