Abstract
Localization properties of fields in compact extra dimensions are crucial ingredients for string model building, particularly in the framework of orbifold compactifications. Realistic models often require a slight deviation from the orbifold point, that can be analyzed using field theoretic methods considering (singlet) fields with nontrivial vacuum expectation values. Some of these fields correspond to blow-up modes that represent the resolution of orbifold singularities. Improving on previous analyses we give here an explicit example of the blow-up of a model from the heterotic Mini-landscape. An exact identification of the blow-up modes at various fixed points and fixed tori with orbifold twisted fields is given. We match the massless spectra and identify the blow-up modes as non-universal axions of compactified string theory. We stress the important role of the Green-Schwarz anomaly polynomial for the description of the resolution of orbifold singularities.
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O. Lebedev, H.P. Nilles, S. Raby, S. Ramos-Sanchez, M. Ratz et al., A mini-landscape of exact MSSM spectra in heterotic orbifolds, Phys. Lett. B 645 (2007) 88 [hep-th/0611095] [INSPIRE].
S. Förste, H.P. Nilles, P.K. Vaudrevange and A. Wingerter, Heterotic brane world, Phys. Rev. D 70 (2004) 106008 [hep-th/0406208] [INSPIRE].
T. Kobayashi, S. Raby and R.-J. Zhang, Searching for realistic 4d string models with a Pati-Salam symmetry: orbifold grand unified theories from heterotic string compactification on a Z 6 orbifold, Nucl. Phys. B 704 (2005) 3 [hep-ph/0409098] [INSPIRE].
W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Dual models of gauge unification in various dimensions, Nucl. Phys. B 712 (2005) 139 [hep-ph/0412318] [INSPIRE].
W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Supersymmetric standard model from the heterotic string, Phys. Rev. Lett. 96 (2006) 121602 [hep-ph/0511035] [INSPIRE].
H.P. Nilles, S. Ramos-Sanchez and P.K. Vaudrevange, Local grand unification and string theory, AIP Conf. Proc. 1200 (2010) 226 [arXiv:0909.3948] [INSPIRE].
H.P. Nilles, S. Ramos-Sanchez, M. Ratz and P.K. Vaudrevange, From strings to the MSSM, Eur. Phys. J. C 59 (2009) 249 [arXiv:0806.3905] [INSPIRE].
W. Buchmüller, K. Hamaguchi, O. Lebedev and M. Ratz, Local grand unification, hep-ph/0512326 [INSPIRE].
T. Kobayashi, H.P. Nilles, F. Ploger, S. Raby and M. Ratz, Stringy origin of non-abelian discrete flavor symmetries, Nucl. Phys. B 768 (2007) 135 [hep-ph/0611020] [INSPIRE].
N.G. Cabo Bizet, T. Kobayashi, D.K. Mayorga Pena, S.L. Parameswaran, M. Schmitz et al., R-charge conservation and more in factorizable and non-factorizable orbifolds, JHEP 05 (2013) 076 [arXiv:1301.2322] [INSPIRE].
R. Kappl, H.P. Nilles, S. Ramos-Sanchez, M. Ratz, K. Schmidt-Hoberg et al., Large hierarchies from approximate R symmetries, Phys. Rev. Lett. 102 (2009) 121602 [arXiv:0812.2120] [INSPIRE].
S. Förste, H.P. Nilles, S. Ramos-Sanchez and P.K. Vaudrevange, Proton hexality in local grand unification, Phys. Lett. B 693 (2010) 386 [arXiv:1007.3915] [INSPIRE].
H.M. Lee, S. Raby, M. Ratz, G.G. Ross, R. Schieren et al., A unique \( Z_4^R \) symmetry for the MSSM, Phys. Lett. B 694 (2011) 491 [arXiv:1009.0905] [INSPIRE].
P. Ko, T. Kobayashi, J.-h. Park and S. Raby, String-derived D 4 flavor symmetry and phenomenological implications, Phys. Rev. D 76 (2007) 035005 [Erratum ibid. D 76 (2007) 059901] [arXiv:0704.2807] [INSPIRE].
J. Casas and C. Muñoz, A natural solution to the μ problem, Phys. Lett. B 306 (1993) 288 [hep-ph/9302227] [INSPIRE].
I. Antoniadis, E. Gava, K. Narain and T. Taylor, Effective mu term in superstring theory, Nucl. Phys. B 432 (1994) 187 [hep-th/9405024] [INSPIRE].
O. Lebedev, H.P. Nilles, S. Raby, S. Ramos-Sanchez, M. Ratz et al., The heterotic road to the MSSM with R parity, Phys. Rev. D 77 (2008) 046013 [arXiv:0708.2691] [INSPIRE].
S. Hamidi and C. Vafa, Interactions on orbifolds, Nucl. Phys. B 279 (1987) 465 [INSPIRE].
P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum configurations for superstrings, Nucl. Phys. B 258 (1985) 46 [INSPIRE].
J. Erler and A. Klemm, Comment on the generation number in orbifold compactifications, Commun. Math. Phys. 153 (1993) 579 [hep-th/9207111] [INSPIRE].
P.S. Aspinwall, Resolution of orbifold singularities in string theory, hep-th/9403123 [INSPIRE].
S. Reffert, Toroidal orbifolds: resolutions, orientifolds and applications in string phenomenology, hep-th/0609040 [INSPIRE].
D. Lüst, S. Reffert, E. Scheidegger and S. Stieberger, Resolved toroidal orbifolds and their orientifolds, Adv. Theor. Math. Phys. 12 (2008) 67 [hep-th/0609014] [INSPIRE].
S. Groot Nibbelink, M. Trapletti and M. Walter, Resolutions of C n/Zn orbifolds, their U(1) bundles and applications to string model building, JHEP 03 (2007) 035 [hep-th/0701227] [INSPIRE].
S. Nibbelink Groot, T.-W. Ha and M. Trapletti, Toric resolutions of heterotic orbifolds, Phys. Rev. D 77 (2008) 026002 [arXiv:0707.1597] [INSPIRE].
T. Kobayashi, S.L. Parameswaran, S. Ramos-Sanchez and I. Zavala, Revisiting coupling selection rules in heterotic orbifold models, JHEP 05 (2012) 008 [Erratum ibid. 1212 (2012) 049] [arXiv:1107.2137] [INSPIRE].
E. Witten, Search for a realistic Kaluza-Klein theory, Nucl. Phys. B 186 (1981) 412 [INSPIRE].
E. Witten, Some properties of O(32) superstrings, Phys. Lett. B 149 (1984) 351 [INSPIRE].
C. Froggatt and H.B. Nielsen, Hierarchy of quark masses, Cabibbo angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].
W. Fischler, H.P. Nilles, J. Polchinski, S. Raby and L. Susskind, Vanishing renormalization of the D term in supersymmetric U(1) theories, Phys. Rev. Lett. 47 (1981) 757 [INSPIRE].
J.J. Atick, L.J. Dixon and A. Sen, String calculation of Fayet-Iliopoulos D terms in arbitrary supersymmetric compactifications, Nucl. Phys. B 292 (1987) 109 [INSPIRE].
M. Dine, N. Seiberg and E. Witten, Fayet-Iliopoulos terms in string theory, Nucl. Phys. B 289 (1987) 589 [INSPIRE].
A. Font, L.E. Ibáñez, H.P. Nilles and F. Quevedo, Yukawa couplings in degenerate orbifolds: towards a realistic SU(3) × SU(2) × U (1) superstring, Phys. Lett. B 210 (1988) 101 [Erratum ibid. B 213 (1988) 564] [INSPIRE].
C. Lüdeling, F. Ruehle and C. Wieck, Non-universal anomalies in heterotic string constructions, Phys. Rev. D 85 (2012) 106010 [arXiv:1203.5789] [INSPIRE].
T. Oda, Convex bodies and algebraic geometry, Springer-Verlag, Berlin Germany (1988).
W. Fulton, Introduction to toric varieties, Annals of mathematics studies 131, Princeton University Press, Princeton U.S.A. (1997).
K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas et al., Mirror symmetry, AMS publications (2003).
S. Nibbelink Groot, D. Klevers, F. Ploger, M. Trapletti and P.K. Vaudrevange, Compact heterotic orbifolds in blow-up, JHEP 04 (2008) 060 [arXiv:0802.2809] [INSPIRE].
S. Nibbelink Groot, J. Held, F. Ruehle, M. Trapletti and P.K. Vaudrevange, Heterotic \( \mathbb{Z} \)(6 − II) MSSM orbifolds in blowup, JHEP 03 (2009) 005 [arXiv:0901.3059] [INSPIRE].
S. Nibbelink Groot, Heterotic orbifold resolutions as (2, 0) gauged linear σ-models, Fortsch. Phys. 59 (2011) 454 [arXiv:1012.3350] [INSPIRE].
M. Blaszczyk, S. Nibbelink Groot and F. Ruehle, Green-Schwarz mechanism in heterotic (2, 0) gauged linear σ-models: torsion and NS5 branes, JHEP 08 (2011) 083 [arXiv:1107.0320] [INSPIRE].
M. Blaszczyk, S. Groot Nibbelink and F. Ruehle, Gauged linear σ-models for toroidal orbifold resolutions, JHEP 05 (2012) 053 [arXiv:1111.5852] [INSPIRE].
M. Blaszczyk, S. Nibbelink Groot, F. Ruehle, M. Trapletti and P.K. Vaudrevange, Heterotic MSSM on a resolved orbifold, JHEP 09 (2010) 065 [arXiv:1007.0203] [INSPIRE].
W. Buchmüller, J. Louis, J. Schmidt and R. Valandro, Voisin-Borcea manifolds and heterotic orbifold models, JHEP 10 (2012) 114 [arXiv:1208.0704] [INSPIRE].
O. Lebedev, H.P. Nilles, S. Ramos-Sanchez, M. Ratz and P.K. Vaudrevange, Heterotic mini-landscape. (II). Completing the search for MSSM vacua in a Z 6 orbifold, Phys. Lett. B 668 (2008) 331 [arXiv:0807.4384] [INSPIRE].
J.E. Kim, J.-H. Kim and B. Kyae, Superstring standard model from Z 12(I) orbifold compactification with and without exotics and effective R-parity, JHEP 06 (2007) 034 [hep-ph/0702278] [INSPIRE].
M. Blaszczyk, S. Nibbelink Groot, M. Ratz, F. Ruehle, M. Trapletti et al., A Z 2 × Z 2 standard model, Phys. Lett. B 683 (2010) 340 [arXiv:0911.4905] [INSPIRE].
C. Vafa and E. Witten, On orbifolds with discrete torsion, J. Geom. Phys. 15 (1995) 189 [hep-th/9409188] [INSPIRE].
F. Ploger, S. Ramos-Sanchez, M. Ratz and P.K. Vaudrevange, Mirage torsion, JHEP 04 (2007) 063 [hep-th/0702176] [INSPIRE].
S. Groot Nibbelink, H.P. Nilles and M. Trapletti, Multiple anomalous U(1)s in heterotic blow-ups, Phys. Lett. B 652 (2007) 124 [hep-th/0703211] [INSPIRE].
F. Gmeiner, S. Groot Nibbelink, H.P. Nilles, M. Olechowski and M. Walter, Localized anomalies in heterotic orbifolds, Nucl. Phys. B 648 (2003) 35 [hep-th/0208146] [INSPIRE].
M.B. Green and J.H. Schwarz, Anomaly cancellation in supersymmetric D = 10 gauge theory and superstring theory, Phys. Lett. B 149 (1984) 117 [INSPIRE].
A. Schellekens and N. Warner, Anomalies, characters and strings, Nucl. Phys. B 287 (1987) 317 [INSPIRE].
M. Blaszczyk, N.G. Cabo Bizet, H.P. Nilles and F. Ruhle, A perfect match of MSSM-like orbifold and resolution models via anomalies, JHEP 10 (2011) 117 [arXiv:1108.0667] [INSPIRE].
D. Bailin and A. Love, Orbifold compactifications of string theory, Phys. Rept. 315 (1999) 285 [INSPIRE].
L.E. Ibáñez, H.P. Nilles and F. Quevedo, Orbifolds and Wilson lines, Phys. Lett. B 187 (1987) 25 [INSPIRE].
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on orbifolds, Nucl. Phys. B 261 (1985) 678 [INSPIRE].
L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on orbifolds. 2., Nucl. Phys. B 274 (1986) 285 [INSPIRE].
L.J. Dixon, D. Friedan, E.J. Martinec and S.H. Shenker, The conformal field theory of orbifolds, Nucl. Phys. B 282 (1987) 13 [INSPIRE].
M.B. Green, J.H. Schwarz, and E. Witten, Superstring theory, vol. 2, Cambridge University Press, Cambridge U.K. (1999).
R. Blumenhagen, G. Honecker and T. Weigand, Loop-corrected compactifications of the heterotic string with line bundles, JHEP 06 (2005) 020 [hep-th/0504232] [INSPIRE].
N.G. Cabo Bizet, Matching the heterotic string in orbifolds and their resolutions, Ph.D. Thesis, University of Bonn (November 2012).
S. Groot Nibbelink and P.K. Vaudrevange, Schoen manifold with line bundles as resolved magnetized orbifolds, JHEP 03 (2013) 142 [arXiv:1212.4033] [INSPIRE].
H.P. Nilles, S. Ramos-Sanchez, P.K. Vaudrevange and A. Wingerter, The orbifolder: a tool to study the low energy effective theory of heterotic orbifolds, Comput. Phys. Commun. 183 (2012) 1363 [arXiv:1110.5229] [INSPIRE].
K.-S. Choi and J.E. Kim, Quarks and leptons from orbifolded superstring, Lect. Notes Phys. 696 (2006) 1.
S.L. Parameswaran, S. Ramos-Sanchez and I. Zavala, On moduli stabilisation and de Sitter vacua in MSSM heterotic orbifolds, JHEP 01 (2011) 071 [arXiv:1009.3931] [INSPIRE].
R. Blumenhagen, G. Honecker and T. Weigand, Supersymmetric (non-)abelian bundles in the type I and SO(32) heterotic string, JHEP 08 (2005) 009 [hep-th/0507041] [INSPIRE].
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ArXiv ePrint: 1302.1989
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Bizet, N.G.C., Nilles, H.P. Heterotic mini-landscape in blow-up. J. High Energ. Phys. 2013, 74 (2013). https://doi.org/10.1007/JHEP06(2013)074
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DOI: https://doi.org/10.1007/JHEP06(2013)074