nLab type II supergravity

Idea

Type II supergravity is a supergravity in dimension 10 which is the low-energy effective quantum field theory underlying type II string theory.

Related concepts

• massive type IIA supergravity

• type II supergravity Lie 2-algebra

• type II geometry, generalized complex geometry

• T-duality, double field theory

• 11-dimensional supergravity

• heterotic supergravity,

• 7-dimensional supergravity

• 5-dimensional supergravity

• 4-dimensional supergravity

• 3-dimensional supergravity

• duality between M-theory and type IIA string theory

• string theory FAQ – Does string theory predict supersymmetry?

References

General

Original constructions (mostly of type IIA):

• F. Giani, M. Pernici, $N=2$ supergravity in ten dimensions, Phys. Rev. D 30 (1984) 325 [doi:10.1103/PhysRevD.30.325]

• M. Huq, M. A. Namazie, Kaluza-Klein supergravity in ten dimensions, Classical and Quantum Gravity 2 3 (1985) [doi:10.1088/0264-9381/2/3/007]

• I. C. G. Campbell, Peter C. West $N = 2$, $D = 10$ non-chiral supergravity and its spontaneous compactification, Nuclear Physics B 243 1 (1984) 112-124 [doi:10.1016/0550-3213(84)90388-2]

Discussion on superspace:

• James L. Carr, S. James Gates Jr., Robert N. Oerter: $D = 10$, $N = 2a$ Supergravity in Superspace, Physics Letters B 189 1–2 (1987) 68-74 [doi:10.1016/0370-2693(87)91271-8, spire:235791]

• Martin Cederwall, Alexander von Gussich, Bengt E. W. Nilsson, Per Sundell, Anders Westerberg: The Dirichlet Super-$p$-Branes in Ten-Dimensional Type IIA and IIB Supergravity, Nucl. Phys. B 490 (1997) 179-201 &lbrackarXiv:hep-th/9611159, doi:10.1016/S0550-3213(97)00075-8]

• Riccardo D'Auria, Pietro Fré, Pietro A. Grassi, Mario Trigiante: Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds, J. High Energy Physics 2008 07 (2008) [arXiv:0803.1703, doi:10.1088/1126-6708/2008/07/059]

See also the general references at supergravity.

• Joseph Polchinski, chapter 12.1 of String Theory Vol 2: Superstring and beyond_, Cambridge Monographs on Mathematical Physics (1998)

Construction of type IIA supergravity via KK-compactification from 11d supergravity:

• M. Huq, M. A. Namazie, Kaluza-Klein Supergravity In Ten Dimensions, Class. Quantum Grav. 2 (1985) 293 (spire:196711)

• Riccardo D'Auria, Pietro Fré, Pietro Grassi, Trigiante, Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds arXiv:0803.1703

Explicit self-dual formulations

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

Solutions and BPS states

Disucssion of black hole solutions (see also at black holes in string theory) includes

• U. Gran, Jan Gutowski, George Papadopoulos, IIB black hole horizons with five-form flux and extended supersymmetry, JHEP 1109:047,2011 (arXiv:1104.2908)

Discussion of black branes and BPS states for type II supergravity includes

• Andrew Callister, Douglas Smith, Topological BPS charges in 10 and 11-dimensional supergravity, Phys. Rev. D78:065042,2008 (arXiv:0712.3235)

• Andrew Callister, Douglas Smith, Topological charges in $SL(2,\mathbb{R})$ covariant massive 11-dimensional and Type IIB SUGRA, Phys.Rev.D80:125035,2009 (arXiv:0907.3614)

• Andrew Callister, Topological BPS charges in 10- and 11-dimensional supergravity, thesis 2010 (spire)

• A. A. Golubtsova, V.D. Ivashchuk, BPS branes in 10 and 11 dimensional supergravity, talk at DIAS 2013 (pdf slides)

Discussion of asymptotic de Sitter spacetimes from time-dependent KK-compactification of type II supergravity:

• Paul Marconnet, Dimitrios Tsimpis, Universal accelerating cosmologies from 10d supergravity, J. High Energ. Phys. 2023 33 (2023) [arXiv:2210.10813, doi:10.1007/JHEP01(2023)033]

• Paul Marconnet, Dimitrios Tsimpis: Universal Cosmologies [arXiv:2505.03449]

reviewed in:

• Dimitrios Tsimpis, Universal accelerating cosmologies from 10d supergravity, talk at M-Theory and Mathematics 2023, NYU Abu Dhabi (Jan 2023) [web]

In terms of (exceptional) generalized complex geometry

A relation of the U-duality symmetry to generalized complex geometry is discussed in

• André Coimbra, Charles Strickland-Constable, Daniel Waldram, Supergravity as Generalised Geometry I: Type II Theories (arXiv:1107.1733)

• Paulo Pires Pacheco, Daniel Waldram, M-theory, exceptional generalised geometry and superpotentials (arXiv:0804.1362)

A thesis reviewing some aspects is

• Nicholas Houston, Supergravity and Generalized Geometry Thesis (2010) (pdf)

Higher curvature corrections

On higher curvature corrections:

• James Liu, Ruben Minasian, Raffaele Savelli, Andreas Schachner, Type IIB at eight derivatives: insights from Superstrings, Superfields and Superparticles $[$arXiv:2205.11530$]$

Via double field theory

Discusdion of type IIA and IIB supergravities via double field theory:

• Olaf Hohm, Seung Ki Kwak, Barton Zwiebach, Unification of Type II Strings and T-duality (arXiv:1106.5452)

and, to the full order in fermions, in

• Imtak Jeon, Kanghoon Lee, Jeong-Hyuck Park, Yoonji Suh, Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory (arxiv:1210.5078)

Comprehensive discussion in higher differential geometry:

• Luigi Alfonsi, Global Double Field Theory is Higher Kaluza-Klein Theory, Fortsch. d. Phys. 2020 (arXiv:1912.07089, doi:10.1002/prop.202000010)

• Luigi Alfonsi, The puzzle of global Double Field Theory: open problems and the case for a Higher Kaluza-Klein perspective (arXiv:2007.04969)

  (relating Kaluza-Klein compactification on principal ∞-bundles to double field theory, T-folds, non-abelian T-duality, type II geometry, exceptional geometry, …)