Supersymmetric backgrounds from generalized Calabi–Yau manifolds

Mariana Graña; Ruben Minasian; Michela Petrini; Alessandro Tomasiello

doi:10.1016/j.crhy.2004.09.010

String theory and fundamental forces/Théorie des cordes et forces fondamentales

Supersymmetric backgrounds from generalized Calabi–Yau manifolds
[Fonds supersymetriques à partir de variétés de Calabi–Yau généralisées.]

Présenté par : Guy Laval

Mariana Graña ¹ ; Ruben Minasian ² ; Michela Petrini ³ ; Alessandro Tomasiello ²

¹ Laboratoire de physique théorique, École normale supérieure, 24, rue Lhomond 75231 Paris cedex 05, France
² Centre de physique théorique, École polytechnique, 91128 Palaiseau cedex, France
³ Laboratoire de mathématiques et physique théorique, université François Rabelais, parc de Grandmont, 37200 Tours, France

Comptes Rendus. Physique, String theory and fundamental forces - Strings 04, part I, Volume 5 (2004) no. 9-10, pp. 979-986.

Résumé
Abstract

On montre que les transformations de supersymétrie pour les théories des cordes de type II peuvent être traduites dans des équations différentielles pour une paire de spineurs purs, l'exponentiel de la forme de Kähler $e^{i J}$ et la forme holomorphe Ω. Ces équations sont symétriques sous l'échange des deux spineurs purs et des formes de RR de rang pair ou impair. Cette propriété est la symétrie miroir pour les variétés avec torsion. On voit aussi que les fluxes de RR entrent seulement dans une des deux équations : $e^{i J}$ est fermé sous l'action de la dérivée extérieure « twisted » dans la corde de type IIA, et de la même manière Ω est fermé en type IIB. Cela implique que les variétés supersymétriques de structure SU(3) sont toujours complexes en type IIB ou bien symplectiques « twisted » en IIA. Ces variétés sont donc des variétés des Calabi–Yau généralisées selon la définition de Hitchin, mais avec une action du champ B différente.

We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kähler form $e^{i J}$ and the holomorphic form Ω. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Moreover, RR fluxes affect only one of the two equations: $e^{i J}$ is closed under the action of the twisted exterior derivative in IIA theory, and similarly Ω is closed in IIB. This means that supersymmetric SU(3)-structure manifolds are always complex in IIB while they are twisted symplectic in IIA. Modulo a different action of the B-field, these are all generalized Calabi–Yau manifolds, as defined by Hitchin.

Publié le : 2004-11-01

DOI : 10.1016/j.crhy.2004.09.010

Keywords: Supersymmetric backgrounds, Generalized Calabi–Yau manifolds
Mots-clés : Fonds supersymetriques, Variétés de Calabi–Yau généralisées

Affiliations des auteurs :

Mariana Graña ¹ ; Ruben Minasian ² ; Michela Petrini ³ ; Alessandro Tomasiello ²

¹ Laboratoire de physique théorique, École normale supérieure, 24, rue Lhomond 75231 Paris cedex 05, France
² Centre de physique théorique, École polytechnique, 91128 Palaiseau cedex, France
³ Laboratoire de mathématiques et physique théorique, université François Rabelais, parc de Grandmont, 37200 Tours, France

@article{CRPHYS_2004__5_9-10_979_0,
     author = {Mariana Gra\~na and Ruben Minasian and Michela Petrini and Alessandro Tomasiello},
     title = {Supersymmetric backgrounds from generalized {Calabi{\textendash}Yau} manifolds},
     journal = {Comptes Rendus. Physique},
     pages = {979--986},
     publisher = {Elsevier},
     volume = {5},
     number = {9-10},
     year = {2004},
     doi = {10.1016/j.crhy.2004.09.010},
     language = {en},
}

TY  - JOUR
AU  - Mariana Graña
AU  - Ruben Minasian
AU  - Michela Petrini
AU  - Alessandro Tomasiello
TI  - Supersymmetric backgrounds from generalized Calabi–Yau manifolds
JO  - Comptes Rendus. Physique
PY  - 2004
SP  - 979
EP  - 986
VL  - 5
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crhy.2004.09.010
LA  - en
ID  - CRPHYS_2004__5_9-10_979_0
ER  -

%0 Journal Article
%A Mariana Graña
%A Ruben Minasian
%A Michela Petrini
%A Alessandro Tomasiello
%T Supersymmetric backgrounds from generalized Calabi–Yau manifolds
%J Comptes Rendus. Physique
%D 2004
%P 979-986
%V 5
%N 9-10
%I Elsevier
%R 10.1016/j.crhy.2004.09.010
%G en
%F CRPHYS_2004__5_9-10_979_0

Mariana Graña; Ruben Minasian; Michela Petrini; Alessandro Tomasiello. Supersymmetric backgrounds from generalized Calabi–Yau manifolds. Comptes Rendus. Physique, String theory and fundamental forces - Strings 04, part I, Volume 5 (2004) no. 9-10, pp. 979-986. doi : 10.1016/j.crhy.2004.09.010. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2004.09.010/

Bibliographie
Cité par

[1] C. Vafa Superstrings and topological strings at large N, J. Math. Phys., Volume 42 (2001), p. 2798 | arXiv

[2] S. Kachru; M.B. Schulz; P.K. Tripathy; S.P. Trivedi New supersymmetric string compactifications, JHEP, Volume 03 (2003), p. 061 | arXiv

[3] S. Gurrieri; J. Louis; A. Micu; D. Waldram Mirror symmetry in generalized Calabi–Yau compactifications, Nucl. Phys. B, Volume 654 (2003), p. 61 | arXiv

[4] S. Fidanza; R. Minasian; A. Tomasiello Mirror symmetric SU(3)-structure manifolds with NS fluxes | arXiv

[5] O. Ben-Bassat Mirror symmetry and generalized complex manifolds | arXiv

[6] N. Hitchin Generalized Calabi–Yau manifolds | arXiv

[7] R. Rohm; E. Witten The antisymmetric tensor field in superstring theory, Ann. Phys., Volume 170 (1986), p. 454

[8] M. Graña; R. Minasian; M. Petrini; A. Tomasiello Supersymmetric backgrounds from generalized Calabi–Yau manifolds | arXiv

[9] M. Gualtieri Generalized complex geometry, Ph.D. thesis, Oxford University | arXiv

[10] D. Huybrechts Generalized Calabi–Yau structures, K3 surfaces, and B-fields | arXiv

[11] A. Kapustin Topological strings on noncommutative manifolds | arXiv

[12] U. Lindstrom; R. Minasian; A. Tomasiello; M. Zabzine Generalized complex manifolds and supersymmetry | arXiv

[13] A. Kapustin; Y. Li Topological sigma-models with H-flux and twisted generalized complex manifolds | arXiv

[14] E. Bergshoeff; R. Kallosh; T. Ortin; D. Roest; A. Van Proeyen New formulations of $D = 10$ supersymmetry and D8–O8 domain walls, Classical Quant. Grav., Volume 18 (2001), p. 3359 | arXiv

Aybike Çatal-Özer; Emine Diriöz Pin(d, d) covariance of pure spinor equations for supersymmetric vacua and non-Abelian T-duality, Journal of High Energy Physics, Volume 2021 (2021) no. 12 | DOI:10.1007/jhep12(2021)071
C. Jeschek; F. Witt Generalised geometries, constrained critical points and Ramond–Ramond fields, Fortschritte der Physik, Volume 59 (2011) no. 5-6, p. 494 | DOI:10.1002/prop.201000097
Andrei Micu Heterotic type IIA duality with fluxes — towards the complete story, Journal of High Energy Physics, Volume 2010 (2010) no. 10 | DOI:10.1007/jhep10(2010)059
Rhiannon Gwyn; Anke Knauf Conifolds and geometric transitions, Reviews of Modern Physics, Volume 80 (2008) no. 4, p. 1419 | DOI:10.1103/revmodphys.80.1419
Brian Wecht Lectures on nongeometric flux compactifications, Classical and Quantum Gravity, Volume 24 (2007) no. 21, p. S773 | DOI:10.1088/0264-9381/24/21/s03
A. Knauf Geometric transitions on non‐Kähler manifolds, Fortschritte der Physik, Volume 55 (2007) no. 1, p. 5 | DOI:10.1002/prop.200610332
Pietro Antonio Grassi; Matteo Marescotti Flux vacua and supermanifolds, Journal of High Energy Physics, Volume 2007 (2007) no. 01, p. 068 | DOI:10.1088/1126-6708/2007/01/068
Christopher M Hull Generalised geometry for M-theory, Journal of High Energy Physics, Volume 2007 (2007) no. 07, p. 079 | DOI:10.1088/1126-6708/2007/07/079
Ian T Ellwood NS-NS fluxes in Hitchin's generalized geometry, Journal of High Energy Physics, Volume 2007 (2007) no. 12, p. 084 | DOI:10.1088/1126-6708/2007/12/084
Mariana Graña Flux compactifications and generalized geometries, Classical and Quantum Gravity, Volume 23 (2006) no. 21, p. S883 | DOI:10.1088/0264-9381/23/21/s02
Chethan N Gowdigere; Nicholas P Warner Holographic Coulomb branch flows with Script N = 1 supersymmetry, Journal of High Energy Physics, Volume 2006 (2006) no. 03, p. 049 | DOI:10.1088/1126-6708/2006/03/049
Dimitrios Tsimpis M-theory on eight-manifolds revisited: Script N = 1 supersymmetry and generalized Spin(7) structures, Journal of High Energy Physics, Volume 2006 (2006) no. 04, p. 027 | DOI:10.1088/1126-6708/2006/04/027
Jonathan P Hsu; Alexander Maloney; Alessandro Tomasiello Black hole attractors and pure spinors, Journal of High Energy Physics, Volume 2006 (2006) no. 09, p. 048 | DOI:10.1088/1126-6708/2006/09/048
Seok Kim; Piljin Yi A heterotic flux background and calibrated five-branes, Journal of High Energy Physics, Volume 2006 (2006) no. 11, p. 040 | DOI:10.1088/1126-6708/2006/11/040
Mariana Graña The Low Energy Limit of String Theory and its Compactifications with Background Fluxes, Letters in Mathematical Physics, Volume 78 (2006) no. 3, p. 279 | DOI:10.1007/s11005-006-0125-z
Melanie Becker; Keshav Dasgupta; Sheldon Katz; Anke Knauf; Radu Tatar Geometric transitions, flops and non-Kähler manifolds: II, Nuclear Physics B, Volume 738 (2006) no. 1-2, p. 124 | DOI:10.1016/j.nuclphysb.2005.12.023
Keshav Dasgupta; Marc Grisaru; Rhiannon Gwyn; Sheldon Katz; Anke Knauf; Radu Tatar Gauge-gravity dualities, dipoles and new non-Kähler manifolds, Nuclear Physics B, Volume 755 (2006) no. 1-3, p. 21 | DOI:10.1016/j.nuclphysb.2006.07.026
Mariana Graña Flux compactifications in string theory: A comprehensive review, Physics Reports, Volume 423 (2006) no. 3, p. 91 | DOI:10.1016/j.physrep.2005.10.008
Giovanni Villadoro; Fabio Zwirner Script N = 1 effective potential from dual type-IIA D6/O6 orientifolds with general fluxes, Journal of High Energy Physics, Volume 2005 (2005) no. 06, p. 047 | DOI:10.1088/1126-6708/2005/06/047
Oliver DeWolfe; Alexander Giryavets; Shamit Kachru; Washington Taylor Type IIA moduli stabilization, Journal of High Energy Physics, Volume 2005 (2005) no. 07, p. 066 | DOI:10.1088/1126-6708/2005/07/066
Jo Bovy; Dieter Lüst; Dimitrios Tsimpis Script N = 1,2 supersymmetric vacua of IIA supergravity and SU(2) structures, Journal of High Energy Physics, Volume 2005 (2005) no. 08, p. 056 | DOI:10.1088/1126-6708/2005/08/056
Jaume Gomis; David Mateos; Fernando Marchesano An open string landscape, Journal of High Energy Physics, Volume 2005 (2005) no. 11, p. 021 | DOI:10.1088/1126-6708/2005/11/021

Cité par 22 documents. Sources : Crossref

Commentaires - Politique