Abstract
We consider \( \mathcal{N}=\left( {2,0} \right) \) backgrounds of IIB supergravity on eight-manifolds \( {{\mathcal{M}}_8} \) with strict SU(4) structure. We give the explicit solution to the Killing spinor equations as a set of algebraic relations between irreducible SU(4) modules of the fluxes and the torsion classes of \( {{\mathcal{M}}_8} \). One consequence of supersymmetry is that \( {{\mathcal{M}}_8} \) must be complex. We show that the conjecture of arXiv:1010.5789 concerning the correspondence between background supersymmetry equations in terms of generalized pure spinors and generalized calibrations for admissible static, magnetic D-branes, does not capture the full set of supersymmetry equations. We identify the missing constraints and express them in the form of a single pure-spinor equation which is well defined for generic SU(4) × SU(4) backgrounds. This additional equation is given in terms of a certain analytic continuation of the generalized calibration form for codimension-2 static, magnetic D-branes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Lüst, P. Patalong and D. Tsimpis, Generalized geometry, calibrations and supersymmetry in diverse dimensions, JHEP 01 (2011) 063 [arXiv:1010.5789] [INSPIRE].
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math/0209099] [INSPIRE].
M. Gualtieri, Generalized complex geometry, Ph.D. Thesis (advisor: N. Hitchin), math/0401221 [INSPIRE].
P. Koerber, Lectures on Generalized Complex Geometry for Physicists, Fortsch. Phys. 59 (2011) 169 [arXiv:1006.1536] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and A. Tomasiello, Generalized structures of N = 1 vacua, JHEP 11 (2005) 020 [hep-th/0505212] [INSPIRE].
L. Martucci and P. Smyth, Supersymmetric D-branes and calibrations on general N = 1 backgrounds, JHEP 11 (2005) 048 [hep-th/0507099] [INSPIRE].
D. Tsimpis, M-theory on eight-manifolds revisited: N = 1 supersymmetry and generalized Spin(7) structures, JHEP 04 (2006) 027 [hep-th/0511047] [INSPIRE].
C.-I. Lazaroiu and E.-M. Babalic, Geometric algebra techniques in flux compactifications (II), JHEP 06 (2013) 054 [arXiv:1212.6918] [INSPIRE].
J. McOrist, D.R. Morrison and S. Sethi, Geometries, Non-Geometries and Fluxes, Adv. Theor. Math. Phys. 14 (2010) [arXiv:1004.5447] [INSPIRE].
D.D. Joyce, Compact manifolds with special holonomy, Oxford mathematical monographs, Oxford university press (2000).
J.P. Gauntlett, N. Kim, D. Martelli and D. Waldram, Five-branes wrapped on SLAG three cycles and related geometry, JHEP 11 (2001) 018 [hep-th/0110034] [INSPIRE].
J.P. Gauntlett, D. Martelli, S. Pakis and D. Waldram, G structures and wrapped NS5-branes, Commun. Math. Phys. 247 (2004) 421 [hep-th/0205050] [INSPIRE].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, Systematics of IIB spinorial geometry, Class. Quant. Grav. 23 (2006) 1617 [hep-th/0507087] [INSPIRE].
J. Gillard, U. Gran and G. Papadopoulos, The Spinorial geometry of supersymmetric backgrounds, Class. Quant. Grav. 22 (2005) 1033 [hep-th/0410155] [INSPIRE].
U. Gran, J. Gutowski and G. Papadopoulos, The G2 spinorial geometry of supersymmetric IIB backgrounds, Class. Quant. Grav. 23 (2006) 143 [hep-th/0505074] [INSPIRE].
U. Gran, J. Gutowski, G. Papadopoulos and D. Roest, Maximally supersymmetric G-backgrounds of IIB supergravity, Nucl. Phys. B 753 (2006) 118 [hep-th/0604079] [INSPIRE].
G.W. Gibbons, M.B. Green and M.J. Perry, Instantons and seven-branes in type IIB superstring theory, Phys. Lett. B 370 (1996) 37 [hep-th/9511080] [INSPIRE].
J.P. Gauntlett, D. Martelli and D. Waldram, Superstrings with intrinsic torsion, Phys. Rev. D 69 (2004) 086002 [hep-th/0302158] [INSPIRE].
D. Lüst, F. Marchesano, L. Martucci and D. Tsimpis, Generalized non-supersymmetric flux vacua, JHEP 11 (2008) 021 [arXiv:0807.4540] [INSPIRE].
P. Koerber and L. Martucci, D-branes on AdS flux compactifications, JHEP 01 (2008) 047 [arXiv:0710.5530] [INSPIRE].
D. Lüst and D. Tsimpis, Supersymmetric AdS 4 compactifications of IIA supergravity, JHEP 02 (2005) 027 [hep-th/0412250] [INSPIRE].
J.P. Gauntlett, D. Martelli, J. Sparks and D. Waldram, Supersymmetric AdS 5 solutions of type IIB supergravity, Class. Quant. Grav. 23 (2006) 4693 [hep-th/0510125] [INSPIRE].
P. Koerber and D. Tsimpis, Supersymmetric sources, integrability and generalized-structure compactifications, JHEP 08 (2007) 082 [arXiv:0706.1244] [INSPIRE].
A. Tomasiello, Generalized structures of ten-dimensional supersymmetric solutions, JHEP 03 (2012) 073 [arXiv:1109.2603] [INSPIRE].
L. Martucci, Electrified branes, JHEP 02 (2012) 097 [arXiv:1110.0627] [INSPIRE].
D. Tsimpis, Fivebrane instantons and Calabi-Yau fourfolds with flux, JHEP 03 (2007) 099 [hep-th/0701287] [INSPIRE].
G.R. Cavalcanti, New aspects of the dd c -lemma, math/0501406 [INSPIRE].
A. Tomasiello, Reformulating supersymmetry with a generalized Dolbeault operator, JHEP 02 (2008) 010 [arXiv:0704.2613] [INSPIRE].
R. Harvey and H.B. Lawson Jr., Calibrated geometries, Acta Math. 148 (1982) 47.
G. Gibbons and G. Papadopoulos, Calibrations and intersecting branes, Commun. Math. Phys. 202 (1999) 593 [hep-th/9803163] [INSPIRE].
J. Gutowski and G. Papadopoulos, AdS calibrations, Phys. Lett. B 462 (1999) 81 [hep-th/9902034] [INSPIRE].
J. Gutowski, G. Papadopoulos and P. Townsend, Supersymmetry and generalized calibrations, Phys. Rev. D 60 (1999) 106006 [hep-th/9905156] [INSPIRE].
M. Mariño, R. Minasian, G.W. Moore and A. Strominger, Nonlinear instantons from supersymmetric p-branes, JHEP 01 (2000) 005 [hep-th/9911206] [INSPIRE].
P. Koerber, Stable D-branes, calibrations and generalized Calabi-Yau geometry, JHEP 08 (2005) 099 [hep-th/0506154] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1306.2543
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Prins, D., Tsimpis, D. IIB supergravity on manifolds with SU(4) structure and generalized geometry. J. High Energ. Phys. 2013, 180 (2013). https://doi.org/10.1007/JHEP07(2013)180
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2013)180