Abstract
String theory may eventually provide a consistent quantum-mechanical unification of elementary particle physics with gravity. Although there is numerous evidence that superstring theory at its core is a unique theory, it possesses a vast landscape of vacuum states with diverse physical properties. The bulk of this landscape is highly exotic—almost all vacua would not even remotely produce anything resembling our universe. Nevertheless, the prospect of having a unified theory of all fundamental forces and matter particles appearing in nature has spawned a whole discipline, string model building, that already led to countless efforts exploring various corners of the space of string theory ground states. This work contributes to this undertaking, by exhaustively classifying an interesting part of the string landscape given by covariant lattice theories.
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Abe, H., Choi, K.S., Kobayashi, T., Ohki, H., Sakai, M.: Non-Abelian discrete flavor symmetries on orbifolds. Int. J. Mod. Phys. A 26, 4067–4082 (2011). doi:10.1142/S0217751X11054061
Balog, J., Forgacs, P., Horvath, Z., Vecsernyes, P.: Lattice classification of the eight-dimensional chiral heterotic strings. Nucl. Phys. B 334, 431 (1990). doi:10.1016/0550-3213(90)90486-W
Balog, J., Forgacs, P., Vecsernyes, P., Horvath, Z.: Lattice classification of the four-dimensional heterotic strings. Phys. Lett. B 197, 395 (1987). doi:10.1016/0370-2693(87)90407-2
Beye, F.: Chiral four-dimensional heterotic covariant lattices. JHEP 1411, 070 (2014). doi:10.1007/JHEP11(2014)070
Beye, F., Kobayashi, T., Kuwakino, S.: Gauge symmetries in heterotic asymmetric orbifolds. Nucl. Phys. B 875, 599–620 (2013). doi:10.1016/j.nuclphysb.2013.07.018
Beye, F., Kobayashi, T., Kuwakino, S.: Gauge origin of discrete flavor symmetries in heterotic orbifolds. Phys. Lett. B 736, 433–437 (2014). doi:10.1016/j.physletb.2014.07.058
Beye, F., Kobayashi, T., Kuwakino, S.: Three-generation asymmetric orbifold models from heterotic string theory. JHEP 1401, 013 (2014). doi:10.1007/JHEP01(2014)013
Buchmüller, W., Hamaguchi, K., Lebedev, O., Ratz, M.: Supersymmetric standard model from the heterotic string. Phys. Rev. Lett. 96, 121,602 (2006). doi:10.1103/PhysRevLett.96.121602
Buchmüller, W., Hamaguchi, K., Lebedev, O., Ratz, M.: Supersymmetric standard model from the heterotic string (II). Nucl. Phys. B 785, 149–209 (2007). doi:10.1016/j.nuclphysb.2007.06.028
Carter, R.: Conjugacy classes in the Weyl group. Compos. Math. 25, 1–59 (1972)
Casher, A., Englert, F., Nicolai, H., Taormina, A.: Consistent superstrings as solutions of the D = 26 bosonic string theory. Phys. Lett. B 162, 121 (1985). doi:10.1016/0370-2693(85)91072-X
Conway, J.H., Sloane, N.J.A.: Low-dimensional lattices. IV. The mass formula. Proc. R. Soc. Lond. A. Math. Phys. Sci. 419(1857), 259–286 (1988). doi:10.1098/rspa.1988.0107
Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups, 3 edn. Springer, New York (1999). doi:10.1007/978-1-4757-6568-7
Dixon, L.J., Harvey, J.A., Vafa, C., Witten, E.: Strings on orbifolds. Nucl. Phys. B261, 678–686 (1985). doi:10.1016/0550-3213(85)90593-0
Dixon, L.J., Harvey, J.A., Vafa, C., Witten, E.: Strings on orbifolds. 2. Nucl. Phys. B274, 285–314 (1986). doi:10.1016/0550-3213(86)90287-7
Englert, F., Nicolai, H., Schellekens, A.: Superstrings from twentysix-dimensions. Nucl. Phys. B274, 315–348 (1986). doi:10.1016/0550-3213(86)90288-9
Gato-Rivera, B., Schellekens, A.N.: Asymmetric Gepner models: revisited. Nucl. Phys. B841, 100–129 (2010). doi:10.1016/j.nuclphysb.2010.07.020
Gliozzi, F., Scherk, J., Olive, D.I.: Supersymmetry, supergravity theories and the dual spinor model. Nucl. Phys. B 122, 253–290 (1977). doi:10.1016/0550-3213(77)90206-1
Goddard, P., Olive, D.I.: Kac-Moody and Virasoro algebras in relation to quantum physics. Int. J. Mod. Phys. A 1, 303 (1986). doi:10.1142/S0217751X86000149
Grimus, W., Ludl, P.O.: Principal series of finite subgroups of SU(3). J. Phys. A43, 445,209 (2010). doi:10.1088/1751-8113/43/44/445209
Horiguchi, T., Sakamoto, M., Tabuse, M.: Cocycle properties of string theories on orbifolds. Prog. Theor. Phys. Suppl. 110, 229–260 (1992). doi:10.1143/PTPS.110.229
Ibáñez, L.E., Kim, J.E., Nilles, H.P., Quevedo, F.: Orbifold compactifications with three fam-ilies of \(SU(3) \times SU(2) \times U(1)^n\). Phys. Lett. B 191, 282–286 (1987). doi:10.1016/0370-2693(87)90255-3
Ibáñez, L.E., Mas, J., Nilles, H.P., Quevedo, F.: Heterotic strings in symmetric and asymmetric orbifold backgrounds. Nucl. Phys. B 301, 157 (1988). doi:10.1016/0550-3213(88)90166-6
Ibáñez, L.E., Nilles, H.P., Quevedo, F.: Orbifolds and Wilson lines. Phys. Lett. B187, 25–32 (1987). doi:10.1016/0370-2693(87)90066-9
Ito, M., Kuwakino, S., Maekawa, N., Moriyama, S., Takahashi, K., Takei, K., Teraguchi, S., Yamashita, T.: E6 grand unified theory with three generations from heterotic string. Phys. Rev. D83, 091,703 (2011). doi:10.1103/PhysRevD.83.091703
Ito, M., Kuwakino, S., Maekawa, N., Moriyama, S., Takahashi, K., Takei, K., Teraguchi, S., Yamashita, T.: Heterotic \(E_6\) GUTs and partition functions. JHEP 1112, 100 (2011). doi:10.1007/JHEP12(2011)100
Kakushadze, Z., Shiu, G., Tye, S.H.H.: Couplings in asymmetric orbifolds and grand unified string models. Nucl. Phys. B 501, 547–597 (1997). doi:10.1016/S0550-3213(97)00364-7
Kappl, R.: Quark mass hierarchies in heterotic orbifold GUTs. JHEP 1104, 019 (2011). doi:10.1007/JHEP04(2011)019
Kappl, R., Petersen, B., Raby, S., Ratz, M., Schieren, R., Vaudrevange, P.K.S.: String-derived MSSM vacua with residual R symmetries. Nucl. Phys. B 847, 325–349 (2011). doi:10.1016/j.nuclphysb.2011.01.032
Katsuki, Y., Kawamura, Y., Kobayashi, T., Ohtsubo, N., Ono, Y., Tanioka, K.: \(Z(N)\) orbifold models. Nucl. Phys. B 341, 611–640 (1990). doi:10.1016/0550-3213(90)90542-L
Kobayashi, T., Nilles, H.P., Ploger, F., Raby, S., Ratz, M.: Stringy origin of non-Abelian discrete flavor symmetries. Nucl. Phys. B 768, 135–156 (2007). doi:10.1016/j.nuclphysb.2007.01.018
Kobayashi, T., Parameswaran, S.L., Ramos-Sanchez, S., Zavala, I.: Revisiting coupling selection rules in heterotic orbifold models. JHEP 1205, 008 (2012). doi:10.1007/JHEP12(2012)049, 10.1007/JHEP05(2012)008
Kobayashi, T., Raby, S., Zhang, R.J.: Constructing 5-D orbifold grand unified theories from heterotic strings. Phys. Lett. B 593, 262–270 (2004). doi:10.1016/j.physletb.2004.04.058
Kobayashi, T., Raby, S., Zhang, R.J.: 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, 3–55 (2005). doi:10.1016/j.nuclphysb.2004.10.035
Lebedev, O., Nilles, H.P., Raby, S., Ramos-Sanchez, S., Ratz, M., Vaudrevange, P.K.S., Wingerter, A.: A Mini-landscape of exact MSSM spectra in heterotic orbifolds. Phys. Lett. B 645, 88–94 (2007). doi:10.1016/j.physletb.2006.12.012
Lebedev, O., Nilles, H.P., Ramos-Sanchez, S., Ratz, M., Vaudrevange, P.K.S.: Heterotic mini-landscape. (II). Completing the search for MSSM vacua in a Z(6) orbifold. Phys. Lett. B668, 331–335 (2008). doi:10.1016/j.physletb.2008.08.054
Lerche, W., Lüst, D.: Covariant heterotic strings and odd selfdual lattices. Phys. Lett. B 187, 45 (1987). doi:10.1016/0370-2693(87)90069-4
Lerche, W., Lüst, D., Schellekens, A.N.: Ten-dimensional heterotic strings from Niemeier lattices. Phys. Lett. B 181, 71 (1986). doi:10.1016/0370-2693(86)91257-8
Lerche, W., Lüst, D., Schellekens, A.N.: Chiral four-dimensional heterotic strings from selfdual lattices. Nucl. Phys. B 287, 477 (1987). doi:10.1016/0550-3213(87)90115-5
Lerche, W., Nilsson, B.E.W., Schellekens, A.N.: Covariant lattices. Superconformal invariance and strings. Nucl. Phys. B294, 136 (1987). doi:10.1016/0550-3213(87)90577-3
Lerche, W., Schellekens, A.N., Warner, N.P.: Lattices and strings. Phys. Rep. 177, 1 (1989). doi:10.1016/0370-1573(89)90077-X
Lüst, D., Theisen, S.: Four-dimensional heterotic strings: orbifolds and covariant lattices. Nucl. Phys. B 302, 499 (1988). doi:10.1016/0550-3213(88)90212-X
Narain, K.S.: New heterotic string theories in uncompactified dimensions < 10. Phys. Lett. B 169, 41 (1986). doi:10.1016/0370-2693(86)90682-9
Narain, K.S., Sarmadi, M.H., Vafa, C.: Asymmetric orbifolds. Nucl. Phys. B288, 551 (1987). doi:10.1016/0550-3213(87)90228-8
Narain, K.S., Sarmadi, M.H., Vafa, C.: Asymmetric orbifolds: path integral and operator formulations. Nucl. Phys. B 356, 163–207 (1991). doi:10.1016/0550-3213(91)90145-N
Narain, K.S., Sarmadi, M.H., Witten, E.: A note on toroidal compactification of heterotic string theory. Nucl. Phys. B 279, 369 (1987). doi:10.1016/0550-3213(87)90001-0
Nilsson, B.E.W., Roberts, P., Salomonson, P.: Standard model—like string theories from covariant lattices. Phys. Lett. B 222, 35 (1989). doi:10.1016/0370-2693(89)90719-3
Schellekens, A.N., Warner, N.P.: Weyl groups, supercurrents and covariant lattices (1). Nucl. Phys. B 308, 397 (1988). doi:10.1016/0550-3213(88)90570-6
Schellekens, A.N., Warner, N.P.: Weyl groups, supercurrents and covariant lattices (2). Nucl. Phys. B 313, 41 (1989). doi:10.1016/0550-3213(89)90512-9
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Beye, F. (2017). Introduction. In: Chiral Four-Dimensional Heterotic String Vacua from Covariant Lattices. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-0804-7_1
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