×

Heterotic domain wall solutions and \(\mathrm{SU}(3)\) structure manifolds. (English) Zbl 1397.81246

Summary: We examine compactifications of heterotic string theory on manifolds with \(\mathrm{SU}(3)\) structure. In particular, we study \( \mathcal{N} = 1/ 2\) domain wall solutions which correspond to the perturbative vacua of the 4\(D\), \( \mathcal{N} = 1 \) supersymmetric theories associated to these compactifications. We extend work which has appeared previously in the literature in two important regards. Firstly, we include two additional fluxes which have been, heretofore, omitted in the general analysis of this situation. This allows for solutions with more general torsion classes than have previously been found. Secondly, we provide explicit solutions for the fluxes as a function of the torsion classes. These solutions are particularly useful in deciding whether equations such as the Bianchi identities can be solved, in addition to the Killing spinor equations themselves. Our work can be used to straightforwardly decide whether any given \(\mathrm{SU}(3)\) structure on a six-dimensional manifold is associated with a solution to heterotic string theory. To illustrate how to use these results, we discuss a number of examples taken from the literature.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
53C80 Applications of global differential geometry to the sciences

Software:

STRINGVACUA
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Graña, M., Flux compactifications in string theory: a comprehensive review, Phys. Rept., 423, 91, (2006)
[2] Blumenhagen, R.; Körs, B.; Lüst, D.; Stieberger, S., Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rept., 445, 1, (2007)
[3] Koerber, P., Lectures on generalized complex geometry for physicists, Fortsch. Phys., 59, 169, (2011) · Zbl 1210.81084
[4] Bouchard, V.; Donagi, R., An SU(5) heterotic standard model, Phys. Lett., B 633, 783, (2006) · Zbl 1247.81348
[5] Braun, V.; He, Y-H; Ovrut, BA; Pantev, T., A heterotic standard model, Phys. Lett., B 618, 252, (2005) · Zbl 1247.81349
[6] Anderson, LB; He, Y-H; Lukas, A., Heterotic compactification, an algorithmic approach, JHEP, 07, 049, (2007)
[7] Anderson, LB; He, Y-H; Lukas, A., Monad bundles in heterotic string compactifications, JHEP, 07, 104, (2008)
[8] Anderson, LB; Gray, J.; He, Y-H; Lukas, A., Exploring positive monad bundles and a new heterotic standard model, JHEP, 02, 054, (2010) · Zbl 1270.81146
[9] Anderson, LB; Gray, J.; Lukas, A.; Palti, E., Two hundred heterotic standard models on smooth Calabi-Yau threefolds, Phys. Rev., D 84, 106005, (2011)
[10] Braun, V.; Candelas, P.; Davies, R.; Donagi, R., The MSSM spectrum from (0, 2)-deformations of the heterotic standard embedding, JHEP, 05, 127, (2012) · Zbl 1348.81435
[11] Anderson, LB; Gray, J.; Lukas, A.; Palti, E., Heterotic line bundle standard models, JHEP, 06, 113, (2012)
[12] Candelas, P.; Horowitz, GT; Strominger, A.; Witten, E., Vacuum configurations for superstrings, Nucl. Phys., B 258, 46, (1985)
[13] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., The edge of supersymmetry: stability walls in heterotic theory, Phys. Lett., B 677, 190, (2009)
[14] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Stability walls in heterotic theories, JHEP, 09, 026, (2009)
[15] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Stabilizing the complex structure in heterotic Calabi-Yau vacua, JHEP, 02, 088, (2011) · Zbl 1294.81153
[16] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., Stabilizing all geometric moduli in heterotic Calabi-Yau vacua, Phys. Rev., D 83, 106011, (2011)
[17] Anderson, LB; Gray, J.; Lukas, A.; Ovrut, B., The Atiyah class and complex structure stabilization in heterotic Calabi-Yau compactifications, JHEP, 10, 032, (2011) · Zbl 1303.81139
[18] Strominger, A., Superstrings with torsion, Nucl. Phys., B 274, 253, (1986)
[19] Lopes Cardoso, G.; etal., Non-Kähler string backgrounds and their five torsion classes, Nucl. Phys., B 652, 5, (2003) · Zbl 1010.83063
[20] Gurrieri, S.; Lukas, A.; Micu, A., Heterotic on half-flat, Phys. Rev., D 70, 126009, (2004)
[21] Micu, A., Heterotic compactifications and nearly-Kähler manifolds, Phys. Rev., D 70, 126002, (2004)
[22] Carlos, B.; Gurrieri, S.; Lukas, A.; Micu, A., Moduli stabilisation in heterotic string compactifications, JHEP, 03, 005, (2006) · Zbl 1226.81179
[23] Gurrieri, S.; Lukas, A.; Micu, A., Heterotic string compactifications on half-flat manifolds. II, JHEP, 12, 081, (2007) · Zbl 1246.81252
[24] Micu, A., Moduli stabilisation in heterotic models with standard embedding, JHEP, 01, 011, (2010) · Zbl 1269.81144
[25] Becker, K.; Dasgupta, K., Heterotic strings with torsion, JHEP, 11, 006, (2002)
[26] Becker, K.; Becker, M.; Dasgupta, K.; Green, PS, Compactifications of heterotic theory on non-Kähler complex manifolds. 1, JHEP, 04, 007, (2003)
[27] Becker, K.; Becker, M.; Green, PS; Dasgupta, K.; Sharpe, E., Compactifications of heterotic strings on non-Kähler complex manifolds. 2, Nucl. Phys., B 678, 19, (2004) · Zbl 1097.81703
[28] Becker, K.; Tseng, L-S, Heterotic flux compactifications and their moduli, Nucl. Phys., B 741, 162, (2006) · Zbl 1214.81188
[29] Gauntlett, JP; Martelli, D.; Waldram, D., Superstrings with intrinsic torsion, Phys. Rev., D 69, 086002, (2004)
[30] Becker, K.; Becker, M.; Fu, J-X; Tseng, L-S; Yau, S-T, Anomaly cancellation and smooth non-Kähler solutions in heterotic string theory, Nucl. Phys., B 751, 108, (2006) · Zbl 1192.81312
[31] Gran, U.; Papadopoulos, G.; Roest, D., Supersymmetric heterotic string backgrounds, Phys. Lett., B 656, 119, (2007) · Zbl 1246.81249
[32] Becker, K.; Bertinato, C.; Chung, Y-C; Guo, G., Supersymmetry breaking, heterotic strings and fluxes, Nucl. Phys., B 823, 428, (2009) · Zbl 1196.81189
[33] Becker, K.; Sethi, S., Torsional heterotic geometries, Nucl. Phys., B 820, 1, (2009) · Zbl 1194.81185
[34] Louis, J.; Martinez-Pedrera, D.; Micu, A., Heterotic compactifications on SU(2)-structure backgrounds, JHEP, 09, 012, (2009)
[35] Lüst, D.; Tsimpis, D., Supersymmetric ads_{4} compactifications of IIA supergravity, JHEP, 02, 027, (2005)
[36] Lüst, D.; Tsimpis, D., Classes of ads_{4} type IIA/IIB compactifications with SU(3) × SU(3) structure, JHEP, 04, 111, (2009)
[37] Lüst, D.; Tsimpis, D., New supersymmetric ads_{4} type-II vacua, JHEP, 09, 098, (2009)
[38] Bovy, J.; Lüst, D.; Tsimpis, D., N = 1, 2 supersymmetric vacua of IIA supergravity and SU(2) structures, JHEP, 08, 056, (2005)
[39] Kachru, S.; Kallosh, R.; Linde, AD; Trivedi, SP, De Sitter vacua in string theory, Phys. Rev., D 68, 046005, (2003) · Zbl 1244.83036
[40] Balasubramanian, V.; Berglund, P.; Conlon, JP; Quevedo, F., Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP, 03, 007, (2005)
[41] Haack, M.; Lüst, D.; Martucci, L.; Tomasiello, A., Domain walls from ten dimensions, JHEP, 10, 089, (2009)
[42] Mayer, C.; Mohaupt, T., Domain walls, hitchin’s flow equations and G_{2}-manifolds, Class. Quant. Grav., 22, 379, (2005) · Zbl 1067.83550
[43] Smyth, P.; Vaula, S., Domain wall flow equations and SU(3) × SU(3) structure compactifications, Nucl. Phys., B 828, 102, (2010) · Zbl 1203.81160
[44] Johnson, MC; Larfors, M., Field dynamics and tunneling in a flux landscape, Phys. Rev., D 78, 083534, (2008)
[45] Johnson, MC; Larfors, M., An obstacle to populating the string theory landscape, Phys. Rev., D 78, 123513, (2008)
[46] Aguirre, A.; Johnson, MC; Larfors, M., Runaway dilatonic domain walls, Phys. Rev., D 81, 043527, (2010)
[47] Braun, AP; Johansson, N.; Larfors, M.; Walliser, N-O, Restrictions on infinite sequences of type IIB vacua, JHEP, 10, 091, (2011) · Zbl 1303.81149
[48] Danielsson, UH; Johansson, N.; Larfors, M., The world next door: results in landscape topography, JHEP, 03, 080, (2007)
[49] Chialva, D.; Danielsson, UH; Johansson, N.; Larfors, M.; Vonk, M., Deforming, revolving and resolving — new paths in the string theory landscape, JHEP, 02, 016, (2008)
[50] Held, J.; Lüst, D.; Marchesano, F.; Martucci, L., DWSB in heterotic flux compactifications, JHEP, 06, 090, (2010) · Zbl 1288.81110
[51] Held, J., BPS-like potential for compactifications of heterotic M-theory?, JHEP, 10, 136, (2011) · Zbl 1303.81165
[52] Lukas, A.; Matti, C., G-structures and domain walls in heterotic theories, JHEP, 01, 151, (2011) · Zbl 1214.81226
[53] Larfors, M.; Lüst, D.; Tsimpis, D., Flux compactification on smooth, compact three-dimensional toric varieties, JHEP, 07, 073, (2010) · Zbl 1290.81126
[54] N.J. Hitchin, Stable forms and special metrics, math/0107101 [INSPIRE]. · Zbl 1004.53034
[55] Jeschek, C.; Witt, F., Generalised G_{2}-structures and type IIB superstrings, JHEP, 03, 053, (2005)
[56] S. Chiossi and S. Salamon, The intrinsic torsion of SU(3) and G_{2}structures, J. Diff. Geom. (2002) [math/0202282] [INSPIRE]. · Zbl 1024.53018
[57] Gurrieri, S.; Louis, J.; Micu, A.; Waldram, D., Mirror symmetry in generalized Calabi-Yau compactifications, Nucl. Phys., B 654, 61, (2003) · Zbl 1010.81071
[58] Klaput, M.; Lukas, A.; Matti, C., Bundles over nearly-Kähler homogeneous spaces in heterotic string theory, JHEP, 09, 100, (2011) · Zbl 1301.81230
[59] Candelas, P.; Ossa, X., Moduli space of Calabi-Yau manifolds, Nucl. Phys., B 355, 455, (1991) · Zbl 0732.53056
[60] Lüst, D., Compactification of ten-dimensional superstring theories over Ricci flat coset spaces, Nucl. Phys., B 276, 220, (1986)
[61] Castellani, L.; Lüst, D., Superstring compactification on homogeneous coset spaces with torsion, Nucl. Phys., B 296, 143, (1988)
[62] Govindarajan, T.; Joshipura, AS; Rindani, SD; Sarkar, U., Supersymmetric compactification of the heterotic string on coset spaces, Phys. Rev. Lett., 57, 2489, (1986)
[63] Govindarajan, T.; Joshipura, AS; Rindani, SD; Sarkar, U., Coset spaces as alternatives to Calabi-Yau spaces in the presence of gaugino condensation, Int. J. Mod. Phys., A 2, 797, (1987)
[64] Chatzistavrakidis, A.; Manousselis, P.; Zoupanos, G., Reducing the heterotic supergravity on nearly-Kähler coset spaces, Fortsch. Phys., 57, 527, (2009) · Zbl 1171.83364
[65] Chatzistavrakidis, A.; Zoupanos, G., Dimensional reduction of the heterotic string over nearly-Kähler manifolds, JHEP, 09, 077, (2009)
[66] Manousselis, P.; Prezas, N.; Zoupanos, G., Supersymmetric compactifications of heterotic strings with fluxes and condensates, Nucl. Phys., B 739, 85, (2006) · Zbl 1109.81358
[67] Lechtenfeld, O.; Nolle, C.; Popov, AD, Heterotic compactifications on nearly Kähler manifolds, JHEP, 09, 074, (2010) · Zbl 1291.81329
[68] Nolle, C., Homogeneous heterotic supergravity solutions with linear Dilaton, J. Phys. A, A 45, 045402, (2012) · Zbl 1235.83089
[69] P. van Nieuwenhuizen, General theory of coset manifolds and antisymmetric tensors applied to Kaluza-Klein supergravity, in Supersymmetry and supergravity84, Proceedings of the Trieste Spring School, Trieste, Italy April 4-14 1984, World Scientific, Singapore (1985).
[70] Kapetanakis, D.; Zoupanos, G., Coset space dimensional reduction of gauge theories, Phys. Rept., 219, 1, (1992)
[71] Mueller-Hoissen, F.; Stuckl, R., Coset spaces and ten-dimensional unified theories, Class. Quant. Grav., 5, 27, (1988) · Zbl 0637.53100
[72] Koerber, P.; Lüst, D.; Tsimpis, D., Type IIA ads_{4} compactifications on cosets, interpolations and domain walls, JHEP, 07, 017, (2008)
[73] Caviezel, C.; etal., On the cosmology of type IIA compactifications on SU(3)-structure manifolds, JHEP, 04, 010, (2009)
[74] S. Bonanos, Exterior differential calculus, http://library.wolfram.com/infocenter/MathSource/683. · Zbl 0728.53040
[75] Gray, J.; He, Y-H; Ilderton, A.; Lukas, A., STRINGVACUA: a Mathematica package for studying vacuum configurations in string phenomenology, Comput. Phys. Commun., 180, 107, (2009) · Zbl 1198.81156
[76] Gray, J.; He, Y-H; Ilderton, A.; Lukas, A., A new method for finding vacua in string phenomenology, JHEP, 07, 023, (2007)
[77] Gray, J.; He, Y-H; Lukas, A., Algorithmic algebraic geometry and flux vacua, JHEP, 09, 031, (2006)
[78] Larfors, M., Flux compactifications on toric varieties, Fortsch. Phys., 59, 730, (2011) · Zbl 1222.81246
[79] N.J. Hitchin, The geometry of three-forms in six and seven dimensions, math/0010054 [INSPIRE]. · Zbl 1036.53042
[80] F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [INSPIRE].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.