×

zbMATH — the first resource for mathematics

Heterotic MSSM on a resolved orbifold. (English) Zbl 1291.81296
Summary: We construct an MSSM with three generations from the heterotic string compactified on a smooth 6D internal manifold using Abelian gauge fluxes only. The compactification space is obtained as a resolution of the \(T^6 \left/ \mathbb{Z}_2 \times \mathbb{Z}_2 \times \mathbb{Z}_{2,\text{free}} \right.\) orbifold. The \(\mathbb{Z}_{2,\text{free}}\) involution of such a resolution breaks the SU(5) GUT group down to the SM gauge group using a suitably chosen (freely acting) Wilson line. Surprisingly, the spectrum on a given resolution is larger than the one on the corresponding orbifold taking into account the branching and Higgsing due to the blow-up modes. The existence of extra resolution states is closely related to the fact that the resolution procedure is not unique. Rather, the various resolutions are connected to each other by op transitions.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81V22 Unified quantum theories
81V17 Gravitational interaction in quantum theory
83E50 Supergravity
57R18 Topology and geometry of orbifolds
35B44 Blow-up in context of PDEs
PDF BibTeX Cite
Full Text: DOI arXiv
References:
[1] Candelas, P.; Horowitz, GT; Strominger, A.; Witten, E., Vacuum configurations for superstrings, Nucl. Phys., B 258, 46, (1985)
[2] Dixon, LJ; Harvey, JA; Vafa, C.; Witten, E., Strings on orbifolds, Nucl. Phys., B 261, 678, (1985)
[3] Dixon, LJ; Harvey, JA; Vafa, C.; Witten, E., Strings on orbifolds. 2, Nucl. Phys., B 274, 285, (1986)
[4] Donaldson, S., Anti-self-dual Yang-Mills connections over complex algebraic surfaces and stable vector bundles, Proc. London Math. Soc., 50, 1, (1985)
[5] Uhlenbeck, K.; Yau, S., On the existence of Hermitian-Yang-Mills connections in stable vector bundles, Commun. Pure Appl. Math., 39, 257, (1986)
[6] Andreas, B.; Curio, G.; Klemm, A., Towards the standard model spectrum from elliptic Calabi-Yau, Int. J. Mod. Phys., A 19, 1987, (2004)
[7] Donagi, R.; Ovrut, BA; Pantev, T.; Waldram, D., Standard-model bundles, Adv. Theor. Math. Phys., 5, 563, (2002)
[8] Candelas, P.; Horowitz, GT; Strominger, A.; Witten, E., Vacuum configurations for superstrings, Nucl. Phys., B 258, 46, (1985)
[9] Witten, E., Symmetry breaking patterns in superstring models, Nucl. Phys., B 258, 75, (1985)
[10] Donagi, R.; Ovrut, BA; Pantev, T.; Waldram, D., Spectral involutions on rational elliptic surfaces, Adv. Theor. Math. Phys., 5, 499, (2002)
[11] Donagi, R.; Ovrut, BA; Pantev, T.; Waldram, D., Standard-model bundles on non-simply connected Calabi-Yau threefolds, JHEP, 08, 053, (2001)
[12] Braun, V.; He, Y-H; Ovrut, BA; Pantev, T., The exact MSSM spectrum from string theory, JHEP, 05, 043, (2006)
[13] Bouchard, V.; Donagi, R., An SU(5) heterotic standard model, Phys. Lett., B 633, 783, (2006)
[14] Anderson, LB; Gray, J.; He, Y-H; Lukas, A., Exploring positive monad bundles and a new heterotic standard model, JHEP, 02, 054, (2010)
[15] Strominger, A., Superstrings with torsion, Nucl. Phys., B 274, 253, (1986)
[16] Dijkstra, TPT; Huiszoon, LR; Schellekens, AN, Supersymmetric standard model spectra from RCFT orientifolds, Nucl. Phys., B 710, 3, (2005)
[17] Dijkstra, TPT; Huiszoon, LR; Schellekens, AN, Chiral supersymmetric standard model spectra from orientifolds of Gepner models, Phys. Lett., B 609, 408, (2005)
[18] Gato-Rivera, B.; Schellekens, AN, Heterotic weight lifting, Nucl. Phys., B 828, 375, (2010)
[19] B. Gato-Rivera and A.N. Schellekens, Asymmetric Gepner models (revisited), arXiv:1003.6075 [SPIRES].
[20] Faraggi, AE; Nanopoulos, DV; Yuan, K-j, A standard like model in the 4D free fermionic string formulation, Nucl. Phys., B 335, 347, (1990)
[21] Cleaver, GB; Faraggi, AE; Nanopoulos, DV, String derived MSSM and M-theory unification, Phys. Lett., B 455, 135, (1999)
[22] Cleaver, GB; Faraggi, AE; Nanopoulos, DV, A minimal superstring standard model. I: flat directions, Int. J. Mod. Phys., A 16, 425, (2001)
[23] Kiritsis, E.; Schellekens, B.; Tsulaia, M., Discriminating MSSM families in (free-field) Gepner orientifolds, JHEP, 10, 106, (2008)
[24] Ibáñez, LE; Nilles, HP; Quevedo, F., Orbifolds and Wilson lines, Phys. Lett., B 187, 25, (1987)
[25] Ibáñez, LE; Kim, JE; Nilles, HP; Quevedo, F., Orbifold compactifications with three families of SU(3) × SU(2) × U(1)\^{}{\(n\)}, Phys. Lett., B 191, 282, (1987)
[26] Ibáñez, LE; Mas, J.; Nilles, H-P; Quevedo, F., Heterotic strings in symmetric and asymmetric orbifold backgrounds, Nucl. Phys., B 301, 157, (1988)
[27] Buchmüller, W.; Hamaguchi, K.; Lebedev, O.; Ratz, M., Supersymmetric standard model from the heterotic string, Phys. Rev. Lett., 96, 121602, (2006)
[28] Buchmüller, W.; Hamaguchi, K.; Lebedev, O.; Ratz, M., Supersymmetric standard model from the heterotic string. II, Nucl. Phys., B 785, 149, (2007)
[29] Lebedev, O.; etal., A mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett., B 645, 88, (2007)
[30] Lebedev, O.; Nilles, HP; Ramos-Sanchez, S.; Ratz, M.; Vaudrevange, PKS, Heterotic mini-landscape (II): completing the search for MSSM vacua in a Z_{6} orbifold, Phys. Lett., B 668, 331, (2008)
[31] Nibbelink, SG; Held, J.; Ruehle, F.; Trapletti, M.; Vaudrevange, PKS, Heterotic Z6-II MSSM orbifolds in blowup, JHEP, 03, 005, (2009)
[32] Witten, E., Strong coupling expansion of Calabi-Yau compactification, Nucl. Phys., B 471, 135, (1996)
[33] Hebecker, A., Grand unification in the projective plane, JHEP, 01, 047, (2004)
[34] Hebecker, A.; Trapletti, M., Gauge unification in highly anisotropic string compactifications, Nucl. Phys., B 713, 173, (2005)
[35] Donagi, R.; Wendland, K., On orbifolds and free fermion constructions, J. Geom. Phys., 59, 942, (2009)
[36] Blaszczyk, M.; etal., A Z_{2} × Z_{2} standard model, Phys. Lett., B 683, 340, (2010)
[37] R. Kappl, B. Petersen, M. Ratz, R. Schieren and P. Vaudrevange, in preparation (2010).
[38] Blumenhagen, R.; Honecker, G.; Weigand, T., Supersymmetric (non-)abelian bundles in the type-I and SO(32) heterotic string, JHEP, 08, 009, (2005)
[39] Blumenhagen, R.; Honecker, G.; Weigand, T., Loop-corrected compactifications of the heterotic string with line bundles, JHEP, 06, 020, (2005)
[40] Anderson, LB; Gray, J.; Ovrut, B., Yukawa textures from heterotic stability walls, JHEP, 05, 086, (2010)
[41] Ploger, F.; Ramos-Sanchez, S.; Ratz, M.; Vaudrevange, PKS, Mirage torsion, JHEP, 04, 063, (2007)
[42] Groot Nibbelink, S.; Nilles, HP; Trapletti, M., Multiple anomalous U(1)s in heterotic blow-ups, Phys. Lett., B 652, 124, (2007)
[43] J. Held, Resolving the singularities of compact heterotic orbifolds, Master’s thesis, Ruprecht-Karls Universität, Heidelberg Germany (2009), available at the Institutsbiliothek Theoretische Physik Heidelberg Germany.
[44] Lüst, D.; Reffert, S.; Scheidegger, E.; Stieberger, S., Resolved toroidal orbifolds and their orientifolds, Adv. Theor. Math. Phys., 12, 67, (2008)
[45] S. Reffert, Toroidal orbifolds: Resolutions, orientifolds and applications in string phenomenology, hep-th/0609040 [SPIRES].
[46] Nibbelink, SG; Trapletti, M.; Walter, M., Resolutions of C\^{}{n}/Z_{n} orbifolds, their U(1) bundles and applications to string model building, JHEP, 03, 035, (2007)
[47] S.G. Nibbelink, Blowups of heterotic orbifolds using toric geometry, arXiv:0708.1875 [SPIRES].
[48] Nibbelink, SG; Ha, T-W; Trapletti, M., Toric resolutions of heterotic orbifolds, Phys. Rev., D 77, 026002, (2008)
[49] Vafa, C.; Witten, E., On orbifolds with discrete torsion, J. Geom. Phys., 15, 189, (1995)
[50] W. Fulton, Introduction to toric varieties, Annals of mathematics studies 131, The William H. Roever lectures in geometry, Princeton University Press, Princeton U.S.A. (1997).
[51] M. Nakahara, Geometry, topology and physics, Taylor & Francis New York U.S.A. (2003).
[52] P. A. Griffiths and J. Harris, Principles of algebraic geometry, Wiley New York U.S.A. (1994).
[53] Aspinwall, PS; Greene, BR; Morrison, DR, Measuring small distances in N = 2 σ-models, Nucl. Phys., B 420, 184, (1994)
[54] Witten, E., Phases of N = 2 theories in two dimensions, Nucl. Phys., B 403, 159, (1993)
[55] M. Fischer, M. Ratz and P. Vaudrevange, in preparation (2010).
[56] Faraggi, AE; Förste, S.; Timirgaziu, C., Z_{2} × Z_{2} heterotic orbifold models of non factorisable six dimensional toroidal manifolds, JHEP, 08, 057, (2006)
[57] Hull, CM, Actions for (2, 1) σ-models and strings, Nucl. Phys., B 509, 252, (1998)
[58] Honecker, G.; Trapletti, M., Merging heterotic orbifolds and K3 compactifications with line bundles, JHEP, 01, 051, (2007)
[59] Nibbelink, SG; Klevers, D.; Ploger, F.; Trapletti, M.; Vaudrevange, PKS, Compact heterotic orbifolds in blow-up, JHEP, 04, 060, (2008)
[60] Denef, F.; Douglas, MR; Florea, B.; Grassi, A.; Kachru, S., Fixing all moduli in a simple F-theory compactification, Adv. Theor. Math. Phys., 9, 861, (2005)
[61] L. Ahlfors Complex analysis, McGraw-Hill Book Company (1953).
[62] N. Koblitz, Introduction to elliptic curves and modular forms, Graduate texts in mathematics 97, Cambridge University Press, Cambridge U.S.A. (1993).
[63] Donagi, R.; Faraggi, AE, On the number of chiral generations in Z_{2} × Z_{2} orbifolds, Nucl. Phys., B 694, 187, (2004)
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.