×

zbMATH — the first resource for mathematics

Rigid D6-branes on \(T^{6}/({\mathbb Z}_{2} \times {\mathbb Z}_{2M} \times \Omega{\mathcal R})\) with discrete torsion. (English) Zbl 1214.81209
Summary: We give a complete classification of \(T^{6}/({\mathbb Z}_{2} \times {\mathbb Z}_{2M} \times \Omega{\mathcal R})\) orientifolds on factorisable tori and rigid D6-branes on them. The analysis includes the supersymmetry, RR tadpole cancellation and K-theory conditions and complete massless open and closed string spectrum (i.e. non-chiral as well as chiral) for fractional or rigid D6-branes for all inequivalent compactification lattices, without and with discrete torsion. We give examples for each orbifold background, which show that on \({\mathbb Z}_{2} \times {\mathbb Z}_{6}\) and \({\mathbb Z}_{2} \times {\mathbb Z}'_{6}\) there exist completely rigid D6-branes despite the self-intersections of orbifold image cycles. This opens up a new avenue for improved Standard Model building. On the other hand, we show that Standard and GUT model building on the \({\mathbb Z}_{2} \times {\mathbb Z}_{4}\) background is ruled out by simple arguments.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81V22 Unified quantum theories
81V17 Gravitational interaction in quantum theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Nilles, HP, Supersymmetry, supergravity and particle physics, Phys. Rept., 110, 1, (1984)
[2] S.P. Martin, A supersymmetry primer, hep-ph/9709356 [SPIRES].
[3] M.A. Luty, 2004 TASI lectures on supersymmetry breaking, hep-th/0509029 [SPIRES].
[4] Buchmüller, W.; Hamaguchi, K.; Lebedev, O.; Ratz, M., Supersymmetric standard model from the heterotic string, Phys. Rev. Lett., 96, 121602, (2006)
[5] Lebedev, O.; etal., A mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett., B 645, 88, (2007)
[6] Buchmüller, W.; Hamaguchi, K.; Lebedev, O.; Ratz, M., Supersymmetric standard model from the heterotic string II, Nucl. Phys., B 785, 149, (2007)
[7] Lebedev, O.; Nilles, HP; Ramos-Sanchez, S.; Ratz, M.; Vaudrevange, PKS, Heterotic mini-landscape (II): completing the search for MSSM vacua in a \( {\mathbb{Z}_6} \) orbifold, Phys. Lett., B 668, 331, (2008)
[8] Braun, V.; He, Y-H; Ovrut, BA; Pantev, T., The exact MSSM spectrum from string theory, JHEP, 05, 043, (2006)
[9] Bouchard, V.; Donagi, R., An SU(5) heterotic standard model, Phys. Lett., B 633, 783, (2006)
[10] Blumenhagen, R.; Honecker, G.; Weigand, T., Loop-corrected compactifications of the heterotic string with line bundles, JHEP, 06, 020, (2005)
[11] Blumenhagen, R.; Moster, S.; Weigand, T., Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds, Nucl. Phys., B 751, 186, (2006)
[12] Aldazabal, G.; Ibáñez, LE; Quevedo, F.; Uranga, AM, D-branes at singularities: a bottom-up approach to the string embedding of the standard model, JHEP, 08, 002, (2000)
[13] Verlinde, H.; Wijnholt, M., Building the standard model on a D3-brane, JHEP, 01, 106, (2007)
[14] Conlon, JP; Maharana, A.; Quevedo, F., Towards realistic string vacua, JHEP, 05, 109, (2009)
[15] Krippendorf, S.; Dolan, MJ; Maharana, A.; Quevedo, F., D-branes at toric singularities: model building, Yukawa couplings and flavour physics, JHEP, 06, 092, (2010)
[16] Beasley, C.; Heckman, JJ; Vafa, C., GUTs and exceptional branes in F-theory -I, JHEP, 01, 058, (2009)
[17] R. Donagi and M. Wijnholt, Model building with F-theory, arXiv:0802.2969 [SPIRES].
[18] Weigand, T., Lectures on F-theory compactifications and model building, Class. Quant. Grav., 27, 214004, (2010)
[19] Dijkstra, TPT; Huiszoon, LR; Schellekens, AN, Chiral supersymmetric standard model spectra from orientifolds of Gepner models, Phys. Lett., B 609, 408, (2005)
[20] Dijkstra, TPT; Huiszoon, LR; Schellekens, AN, Supersymmetric standard model spectra from RCFT orientifolds, Nucl. Phys., B 710, 3, (2005)
[21] Uranga, AM, Chiral four-dimensional string compactifications with intersecting D-branes, Class. Quant. Grav., 20, 373, (2003)
[22] Blumenhagen, R.; Cvetič, M.; Langacker, P.; Shiu, G., Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci., 55, 71, (2005)
[23] Blumenhagen, R.; Körs, B.; Lüst, D.; Stieberger, S., Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rept., 445, 1, (2007)
[24] Dudas, E., Orientifolds and model building, J. Phys. Conf. Ser., 53, 567, (2006)
[25] Marchesano, F., Progress in D-brane model building, Fortsch. Phys., 55, 491, (2007)
[26] D. Lüst, String landscape and the standard model of particle physics, arXiv:0707.2305 [SPIRES].
[27] Angelantonj, C.; Sagnotti, A., Open strings, Phys. Rept., 371, 1, (2002)
[28] Cvetič, M.; Halverson, J.; Richter, R., Realistic Yukawa structures from orientifold compactifications, JHEP, 12, 063, (2009)
[29] Anastasopoulos, P.; Leontaris, GK; Richter, R.; Schellekens, AN, SU(5) D-brane realizations, Yukawa couplings and proton stability, JHEP, 12, 011, (2010)
[30] Vafa, C., Modular invariance and discrete torsion on orbifolds, Nucl. Phys., B 273, 592, (1986)
[31] Font, A.; Ibáñez, LE; Quevedo, F., \( {\mathbb{Z}_N} × {\mathbb{Z}_M} \) orbifolds and discrete torsion, Phys. Lett., B 217, 272, (1989)
[32] Blumenhagen, R.; Braun, V.; Körs, B.; Lüst, D., Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes, JHEP, 07, 026, (2002)
[33] Blumenhagen, R.; Cvetič, M.; Marchesano, F.; Shiu, G., Chiral D-brane models with frozen open string moduli, JHEP, 03, 050, (2005)
[34] Blumenhagen, R.; Görlich, L.; Ott, T., Supersymmetric intersecting branes on the type IIA \( {{{{T^6}}} \left/ {{{\mathbb{Z}_4}}} \right.} \) orientifold, JHEP, 01, 021, (2003)
[35] Billò, M.; etal., Instantons in N = 2 magnetized D-brane worlds, JHEP, 10, 091, (2007)
[36] Billò, M.; etal., Instanton effects in N = 1 brane models and the Kähler metric of twisted matter, JHEP, 12, 051, (2007)
[37] Blumenhagen, R.; Cvetič, M.; Kachru, S.; Weigand, T., D-brane instantons in type II orientifolds, Ann. Rev. Nucl. Part. Sci., 59, 269, (2009)
[38] Blumenhagen, R.; Cvetič, M.; Weigand, T., Spacetime instanton corrections in 4D string vacua -the seesaw mechanism for D-brane models, Nucl. Phys., B 771, 113, (2007)
[39] Ibáñez, LE; Uranga, AM, Neutrino Majorana masses from string theory instanton effects, JHEP, 03, 052, (2007)
[40] Ibáñez, LE; Richter, R., Stringy instantons and Yukawa couplings in MSSM-like orientifold models, JHEP, 03, 090, (2009)
[41] Abel, SA; Goodsell, MD, Realistic Yukawa couplings through instantons in intersecting brane worlds, JHEP, 10, 034, (2007)
[42] Blumenhagen, R.; Cvetič, M.; Lüst, D.; Richter, R.; Weigand, T., Non-perturbative Yukawa couplings from string instantons, Phys. Rev. Lett., 100, 061602, (2008)
[43] M. Cvetič and T. Weigand, A string theoretic model of gauge mediated supersymmetry beaking, arXiv:0807.3953 [SPIRES].
[44] Marchesano, F., D6-branes and torsion, JHEP, 05, 019, (2006)
[45] Ihl, M.; Wrase, T., Towards a realistic type IIA \( {{{{T^6}}} \left/ {{{\mathbb{Z}_4}}} \right.} \) orientifold model with background fluxes. I: moduli stabilization, JHEP, 07, 027, (2006)
[46] Ihl, M.; Robbins, D.; Wrase, T., Toroidal orientifolds in IIA with general NS-NS fluxes, JHEP, 08, 043, (2007)
[47] Cvetič, M.; Liu, T.; Schulz, MB, Twisting \(K\)3 × \(T\)\^{}{2} orbifolds, JHEP, 09, 092, (2007)
[48] Angelantonj, C.; Cardella, M.; Irges, N., Scherk-Schwarz breaking and intersecting branes, Nucl. Phys., B 725, 115, (2005)
[49] Serone, M.; Trapletti, M., String vacua with flux from freely-acting orbifolds, JHEP, 01, 012, (2004)
[50] Larosa, M.; Pradisi, G., Magnetized four-dimensional \( {\mathbb{Z}_2} × {\mathbb{Z}_2} \) orientifolds, Nucl. Phys., B 667, 261, (2003)
[51] Dudas, E.; Timirgaziu, C., Internal magnetic fields and supersymmetry in orientifolds, Nucl. Phys., B 716, 65, (2005)
[52] Förste, S.; Honecker, G.; Schreyer, R., Supersymmetric \( {\mathbb{Z}_N} × {\mathbb{Z}_M} \) orientifolds in 4D with D-branes at angles, Nucl. Phys., B 593, 127, (2001)
[53] Cvetič, M.; Shiu, G.; Uranga, AM, Three-family supersymmetric standard like models from intersecting brane worlds, Phys. Rev. Lett., 87, 201801, (2001)
[54] Cvetič, M.; Shiu, G.; Uranga, AM, Chiral four-dimensional N = 1 supersymmetric type IIA orientifolds from intersecting D6-branes, Nucl. Phys., B 615, 3, (2001)
[55] Blumenhagen, R.; Gmeiner, F.; Honecker, G.; Lüst, D.; Weigand, T., The statistics of supersymmetric D-brane models, Nucl. Phys., B 713, 83, (2005)
[56] Gmeiner, F.; Blumenhagen, R.; Honecker, G.; Lüst, D.; Weigand, T., One in a billion: MSSM-like D-brane statistics, JHEP, 01, 004, (2006)
[57] Förste, S.; Zavala, I., Oddness from rigidness, JHEP, 07, 086, (2008)
[58] Förste, S.; Timirgaziu, C.; Zavala, I., Orientifold’s landscape: non-factorisable six-tori, JHEP, 10, 025, (2007)
[59] Klein, M.; Rabadán, R., Orientifolds with discrete torsion, JHEP, 07, 040, (2000)
[60] Klein, M.; Rabadán, R., \( {\mathbb{Z}_N} × {\mathbb{Z}_M} \) orientifolds with and without discrete torsion, JHEP, 10, 049, (2000)
[61] Rabadán, R.; Uranga, AM, Type IIB orientifolds without untwisted tadpoles and non-BPS D-branes, JHEP, 01, 029, (2001)
[62] Karp, RL; Esposito, FP; Witten, L., Type IIB orientifolds with discrete torsion, Int. J. Mod. Phys., 16S1C, 978, (2001)
[63] Lüst, D.; Reffert, S.; Scheidegger, E.; Schulgin, W.; Stieberger, S., Moduli stabilization in type IIB orientifolds. II, Nucl. Phys., B 766, 178, (2007)
[64] Honecker, G., Chiral supersymmetric models on an orientifold of \( {\mathbb{Z}_4} × {\mathbb{Z}_2} \) with intersecting D6-branes, Nucl. Phys., B 666, 175, (2003)
[65] G. Honecker, Supersymmetric intersecting D6-branes and chiral models on the\( {{{{T^6}}} \left/ ({{{\mathbb{Z}_4} × {\mathbb{Z}_2}}}) \right.} \)orbifold, hep-th/0309158 [SPIRES].
[66] Cvetič, M.; Langacker, P., New grand unified models with intersecting D6-branes, neutrino masses and flipped SU(5), Nucl. Phys., B 776, 118, (2007)
[67] Honecker, G., Chiral N = 1 4D orientifolds with D-branes at angles, Mod. Phys. Lett., A 19, 1863, (2004)
[68] Gmeiner, F.; Honecker, G., Mapping an island in the landscape, JHEP, 09, 128, (2007)
[69] Gmeiner, F.; Honecker, G., Millions of standard models on \( \mathbb{Z}_6^{′} \)?, JHEP, 07, 052, (2008)
[70] Honecker, G.; Ott, T., Getting just the supersymmetric standard model at intersecting branes on the \( {\mathbb{Z}_6} \)-orientifold, Phys. Rev., D 70, 126010, (2004)
[71] Gmeiner, F.; Lüst, D.; Stein, M., Statistics of intersecting D-brane models on \( {{{{T^6}}} \left/ {{{\mathbb{Z}_6}}} \right.} \), JHEP, 05, 018, (2007)
[72] Lüst, D.; Stieberger, S., Gauge threshold corrections in intersecting brane world models, Fortsch. Phys., 55, 427, (2007)
[73] Akerblom, N.; Blumenhagen, R.; Lüst, D.; Schmidt-Sommerfeld, M., Thresholds for intersecting D-branes revisited, Phys. Lett., B 652, 53, (2007)
[74] Blumenhagen, R.; Schmidt-Sommerfeld, M., Gauge thresholds and Kähler metrics for rigid intersecting D-brane models, JHEP, 12, 072, (2007)
[75] Angelantonj, C.; Condeescu, C.; Dudas, E.; Lennek, M., Stringy instanton effects in models with rigid magnetised D-branes, Nucl. Phys., B 818, 52, (2009)
[76] Conlon, JP, Gauge threshold corrections for local string models, JHEP, 04, 059, (2009)
[77] Conlon, JP; Palti, E., Gauge threshold corrections for local orientifolds, JHEP, 09, 019, (2009)
[78] Conlon, JP; Palti, E., On gauge threshold corrections for local IIB/F-theory guts, Phys. Rev., D 80, 106004, (2009)
[79] Gmeiner, F.; Honecker, G., Complete gauge threshold corrections for intersecting fractional D6-branes: the Z6 and Z6’ standard models, Nucl. Phys., B 829, 225, (2010)
[80] Vafa, C.; Witten, E., A one loop test of string duality, Nucl. Phys., B 447, 261, (1995)
[81] S. Reffert, The Geometer’s Toolkit to String Compactifications, arXiv:0706.1310 [SPIRES].
[82] Gimon, EG; Polchinski, J., Consistency conditions for orientifolds and D-manifolds, Phys. Rev., D 54, 1667, (1996)
[83] Blumenhagen, R.; Görlich, L.; Körs, B., Supersymmetric 4D orientifolds of type IIA with D6-branes at angles, JHEP, 01, 040, (2000)
[84] Angelantonj, C.; Antoniadis, I.; D’Appollonio, G.; Dudas, E.; Sagnotti, A., Type I vacua with brane supersymmetry breaking, Nucl. Phys., B 572, 36, (2000)
[85] Berkooz, M.; Leigh, RG, AD = 4 N = 1 orbifold of type I strings, Nucl. Phys., B 483, 187, (1997)
[86] Uranga, AM, D-brane probes, RR tadpole cancellation and K-theory charge, Nucl. Phys., B 598, 225, (2001)
[87] S. Förste, G. Honecker and G. Sukumaran, Particle physics on\( {{{{T^6}}} \left/ {{{\mathbb{Z}_2} × {\mathbb{Z}_6}}} \right.} \)and\( {{{{T^6}}} \left/ {{{\mathbb{Z}_2} × \mathbb{Z}_6^{′}}} \right.} \)with discrete torsion, work in progress.
[88] Lowen, V.; Nilles, HP, Mirage pattern from the heterotic string, Phys. Rev., D 77, 106007, (2008)
[89] S.L. Parameswaran, S. Ramos-Sanchez and I. Zavala, On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds, arXiv:1009.3931 [SPIRES].
[90] E. Sharpe, Notes on discrete torsion in orientifolds, arXiv:0908.0087 [SPIRES].
[91] Lüst, D.; Stieberger, S.; Taylor, TR, The LHC string hunter’s companion, Nucl. Phys., B 808, 1, (2009)
[92] Lüst, D.; Schlotterer, O.; Stieberger, S.; Taylor, TR, The LHC string hunter’s companion (II): five-particle amplitudes and universal properties, Nucl. Phys., B 828, 139, (2010)
[93] Feng, W-Z; Lüst, D.; Schlotterer, O.; Stieberger, S.; Taylor, TR, Direct production of lightest Regge resonances, Nucl. Phys., B 843, 570, (2011)
[94] R. Blumenhagen, A. Deser and D. Lüst, FCNC processes from D-brane instantons, arXiv:1007.4770 [SPIRES].
[95] Grimm, TW; Louis, J., The effective action of type IIA Calabi-Yau orientifolds, Nucl. Phys., B 718, 153, (2005)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.