Abstract
We study the global structure of vacua of heterotic strings compactified on orbifolds T4/ℤN (N = 2, 3) in the presence of heterotic 5-branes. Gauge symmetry breaking associated with orbifold is described by instantons in the field theory. There is phase transition between small (zero size limit) instantons and heterotic 5-branes. This mechanism provides top-down, stringy account to the spectrum and modular invariance condition of non-perturbative vacua with 5-branes. Also it takes us from one vacuum to another by emitting and absorbing instantons. This means that many vacua with different gauge theories are in fact connected and are inherited from perturbative vacua. It follows that there is also transition of twisted instantons at the fixed points. Thus we can understand transitions among perturbative vacua as well.
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References
E. Witten, Small instantons in string theory, Nucl. Phys.B 460 (1996) 541 [hep-th/9511030] [INSPIRE].
M.J. Duff, R. Minasian and E. Witten, Evidence for heterotic/heterotic duality, Nucl. Phys.B 465 (1996) 413 [hep-th/9601036] [INSPIRE].
O.J. Ganor and A. Hanany, Small E 8instantons and tensionless noncritical strings, Nucl. Phys.B 474 (1996) 122 [hep-th/9602120] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 1, Nucl. Phys.B 473 (1996) 74 [hep-th/9602114] [INSPIRE].
D.R. Morrison and C. Vafa, Compactifications of F-theory on Calabi-Yau threefolds. 2., Nucl. Phys.B 476 (1996) 437 [hep-th/9603161] [INSPIRE].
M. Bershadsky, K.A. Intriligator, S. Kachru, D.R. Morrison, V. Sadov and C. Vafa, Geometric singularities and enhanced gauge symmetries, Nucl. Phys.B 481 (1996) 215 [hep-th/9605200] [INSPIRE].
B. Haghighat, G. Lockhart and C. Vafa, Fusing E-strings to heterotic strings: E + E → H, Phys. Rev.D 90 (2014) 126012 [arXiv:1406.0850] [INSPIRE].
J. Kim, S. Kim, K. Lee, J. Park and C. Vafa, Elliptic Genus of E-strings, JHEP09 (2017) 098 [arXiv:1411.2324] [INSPIRE].
K.-S. Choi and S.-J. Rey, E(lementary) Strings in Six-Dimensional Heterotic F-theory, JHEP09 (2017) 092 [arXiv:1706.05353] [INSPIRE].
K.-S. Choi and S.-J. Rey, Elliptic Genus, Anomaly Cancellation and Heterotic M-theory, arXiv:1710.07627 [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].
M. Berkooz, R.G. Leigh, J. Polchinski, J.H. Schwarz, N. Seiberg and E. Witten, Anomalies, dualities and topology of D = 6 N = 1 superstring vacua, Nucl. Phys.B 475 (1996) 115 [hep-th/9605184] [INSPIRE].
J. Erler, Anomaly cancellation in six-dimensions, J. Math. Phys.35 (1994) 1819 [hep-th/9304104] [INSPIRE].
S. Kachru and C. Vafa, Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys.B 450 (1995) 69 [hep-th/9505105] [INSPIRE].
G. Aldazabal, A. Font, L.E. Ibáñez and F. Quevedo, Chains of N = 2, D = 4 heterotic type-II duals, Nucl. Phys.B 461 (1996) 85 [hep-th/9510093] [INSPIRE].
G. Aldazabal, A. Font, L.E. Ibáñez, A.M. Uranga and G. Violero, Nonperturbative heterotic D=6, D=4, N =1 orbifold vacua,Nucl. Phys.B 519(1998) 239 [hep-th/9706158] [INSPIRE].
K.-S. Choi and J.E. Kim, Z(2) orbifold compactification of heterotic string and 6-D SO(14) flavor unification model, Phys. Lett.B 552 (2003) 81 [hep-th/0206099] [INSPIRE].
G. Honecker and M. Trapletti, Merging Heterotic Orbifolds and K3 Compactifications with Line Bundles, JHEP01 (2007) 051 [hep-th/0612030] [INSPIRE].
C. Lüdeling and F. Ruehle, F-theory duals of singular heterotic K3 models, Phys. Rev.D 91 (2015) 026010 [arXiv:1405.2928] [INSPIRE].
K.A. Intriligator, RG fixed points in six-dimensions via branes at orbifold singularities, Nucl. Phys.B 496 (1997) 177 [hep-th/9702038] [INSPIRE].
T. Eguchi, P.B. Gilkey and A.J. Hanson, Gravitation, Gauge Theories and Differential Geometry, Phys. Rept.66 (1980) 213 [INSPIRE].
P. Candelas, G.T. Horowitz, A. Strominger and E. Witten, Vacuum Configurations for Superstrings, Nucl. Phys.B 258 (1985) 46 [INSPIRE].
K. Dasgupta, G. Rajesh and S. Sethi, M theory, orientifolds and G-flux, JHEP08 (1999) 023 [hep-th/9908088] [INSPIRE].
N. Seiberg and E. Witten, Comments on string dynamics in six-dimensions, Nucl. Phys.B 471 (1996) 121 [hep-th/9603003] [INSPIRE].
A. Sagnotti, A Note on the Green-Schwarz mechanism in open string theories, Phys. Lett.B 294 (1992) 196 [hep-th/9210127] [INSPIRE].
E. Witten, σ-models and the ADHM construction of instantons, J. Geom. Phys.15 (1995) 215 [hep-th/9410052] [INSPIRE].
P. Hořava and E. Witten, Heterotic and type-I string dynamics from eleven-dimensions, Nucl. Phys.B 460 (1996) 506 [hep-th/9510209] [INSPIRE].
P. Hořava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary, Nucl. Phys.B 475 (1996) 94 [hep-th/9603142] [INSPIRE].
S. Groot Nibbelink, M. Trapletti and M. Walter, Resolutions of C n/Z nOrbifolds, their U(1) Bundles and Applications to String Model Building, JHEP03 (2007) 035 [hep-th/0701227] [INSPIRE].
S. Groot Nibbelink, T.-W. Ha and M. Trapletti, Toric Resolutions of Heterotic Orbifolds, Phys. Rev.D 77 (2008) 026002 [arXiv:0707.1597] [INSPIRE].
K.-S. Choi and J.E. Kim, Quarks and leptons from orbifolded superstring, Lect. Notes Phys.696 (2006) 1 [INSPIRE].
L.E. Ibáñez, J. Mas, H.-P. Nilles and F. Quevedo, Heterotic Strings in Symmetric and Asymmetric Orbifold Backgrounds, Nucl. Phys.B 301 (1988) 157 [INSPIRE].
Y. Katsuki, Y. Kawamura, T. Kobayashi, N. Ohtsubo, Y. Ono and K. Tanioka, Z(N) orbifold models, Nucl. Phys.B 341 (1990) 611 [INSPIRE].
K.-S. Choi, S. Groot Nibbelink and M. Trapletti, Heterotic SO(32) model building in four dimensions, JHEP12 (2004) 063 [hep-th/0410232] [INSPIRE].
L.J. Dixon, Symmetry Breaking in String Theories via Orbifolds, Ph.D. Thesis, Princeton University (1986).
K.-S. Choi, K. Hwang and J.E. Kim, Dynkin diagram strategy for orbifolding with Wilson lines, Nucl. Phys.B 662 (2003) 476 [hep-th/0304243] [INSPIRE].
K.S. Narain, New Heterotic String Theories in Uncompactified Dimensions < 10, Phys. Lett.169B (1986) 41 [INSPIRE].
K.S. Narain, M.H. Sarmadi and E. Witten, A Note on Toroidal Compactification of Heterotic String Theory, Nucl. Phys.B 279 (1987) 369 [INSPIRE].
K.-S. Choi, Unification in intersecting brane models, Phys. Rev.D 74 (2006) 066002 [hep-th/0603186] [INSPIRE].
K.-S. Choi, Intersecting brane world from type-I compactification, Int. J. Mod. Phys.A 22 (2007) 3169 [hep-th/0610026] [INSPIRE].
A.N. Schellekens and N.P. Warner, Anomalies and Modular Invariance in String Theory, Phys. Lett.B 177 (1986) 317 [INSPIRE].
A.N. Schellekens and N.P. Warner, Anomaly Cancellation and Selfdual Lattices, Phys. Lett.B 181 (1986) 339 [INSPIRE].
M. Berkooz and R.G. Leigh, A D = 4 N = 1 orbifold of type-I strings, Nucl. Phys.B 483 (1997) 187 [hep-th/9605049] [INSPIRE].
E. Gorbatov, V.S. Kaplunovsky, J. Sonnenschein, S. Theisen and S. Yankielowicz, On heterotic orbifolds, M-theory and type-I-prime brane engineering, JHEP05 (2002) 015 [hep-th/0108135] [INSPIRE].
S. Förste, H.P. Nilles, P.K.S. 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, Constructing 5-D orbifold grand unified theories from heterotic strings, Phys. Lett.B 593 (2004) 262 [hep-ph/0403065] [INSPIRE].
K.S. Choi and T. Kobayashi, work in progress.
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ArXiv ePrint: 1901.11194
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Choi, KS., Kobayashi, T. Transitions of orbifold vacua. J. High Energ. Phys. 2019, 111 (2019). https://doi.org/10.1007/JHEP07(2019)111
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DOI: https://doi.org/10.1007/JHEP07(2019)111