Abstract
We study the effect of quantum corrections on heterotic compactifications on elliptic fibrations away from the stable degeneration limit, elaborating on a recent observation by Malmendier and Morrison. We show that already for the simplest nontrivial elliptic fibration the effect is quite dramatic: the I 1 degeneration with trivial gauge background dynamically splits into two T-fects with monodromy around each T-fect being (conjugate to) T-duality along one of the legs of the T 2. This implies that almost every elliptic heterotic compactification becomes a non-geometric T-fold away from the stable degeneration limit. We also point out a subtlety due to this non-geometric splitting at finite fiber size. It arises when determining, via heterotic/F-theory duality, the SCFTs associated to a small number of pointlike instantons probing heterotic ADE singularities. Along the way we resolve various puzzles in the literature.
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References
E. Witten, Small instantons in string theory, Nucl. Phys. B 460 (1996) 541 [hep-th/9511030] [INSPIRE].
D. Lüst, S. Massai and V. Vall Camell, The monodromy of T-folds and T-fects, JHEP 09 (2016) 127 [arXiv:1508.01193] [INSPIRE].
A. Font, I. García-Etxebarria, D. Lüst, S. Massai and C. Mayrhofer, Heterotic T-fects, 6D SCFTs and F-theory, JHEP 08 (2016) 175 [arXiv:1603.09361] [INSPIRE].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
A. Sen, Orientifold limit of F-theory vacua, Phys. Rev. D 55 (1997) R7345 [hep-th/9702165] [INSPIRE].
T. Banks, M.R. Douglas and N. Seiberg, Probing F-theory with branes, Phys. Lett. B 387 (1996) 278 [hep-th/9605199] [INSPIRE].
F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [INSPIRE].
J. McOrist, D.R. Morrison and S. Sethi, Geometries, non-geometries and fluxes, Adv. Theor. Math. Phys. 14 (2010) 1515 [arXiv:1004.5447] [INSPIRE].
A. Malmendier and D.R. Morrison, K3 surfaces, modular forms and non-geometric heterotic compactifications, Lett. Math. Phys. 105 (2015) 1085 [arXiv:1406.4873] [INSPIRE].
A. Malmendier and T. Shaska, The Satake sextic in elliptic fibrations on K3, arXiv:1609.04341 [INSPIRE].
C. Vafa, Evidence for F-theory, Nucl. Phys. B 469 (1996) 403 [hep-th/9602022] [INSPIRE].
J. Gu and H. Jockers, Nongeometric F-theory-heterotic duality, Phys. Rev. D 91 (2015) 086007 [arXiv:1412.5739] [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].
G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, On the duality between the heterotic string and F-theory in eight-dimensions, Phys. Lett. B 389 (1996) 479 [hep-th/9609111] [INSPIRE].
W. Lerche and S. Stieberger, Prepotential, mirror map and F-theory on K3, Adv. Theor. Math. Phys. 2 (1998) 1105 [Erratum ibid. 3 (1999) 1199] [hep-th/9804176] [INSPIRE].
S. Tetsuji, Kummer sandwich theorem of certain elliptic K3 surfaces, Proc. Jpn. Acad. Ser. A 82 (2006) 137.
A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [INSPIRE].
S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].
M.R. Gaberdiel and B. Zwiebach, Exceptional groups from open strings, Nucl. Phys. B 518 (1998) 151 [hep-th/9709013] [INSPIRE].
E. Witten, Heterotic string conformal field theory and A-D-E singularities, JHEP 02 (2000) 025 [hep-th/9909229] [INSPIRE].
P.S. Aspinwall, Point-like instantons and the Spin(32)/Z 2 heterotic string, Nucl. Phys. B 496 (1997) 149 [hep-th/9612108] [INSPIRE].
A.P. Ogg, On pencils of curves of genus two, Topology 5 (1966) 355.
Y. Namikawa and K. Ueno, The complete classification of fibres in pencils of curves of genus two, Manuscripta Math. 9 (1973) 143.
P.S. Aspinwall and D.R. Morrison, Point-like instantons on K3 orbifolds, Nucl. Phys. B 503 (1997) 533 [hep-th/9705104] [INSPIRE].
A. Hanany and A. Zaffaroni, Branes and six-dimensional supersymmetric theories, Nucl. Phys. B 529 (1998) 180 [hep-th/9712145] [INSPIRE].
R. Friedman, J.W. Morgan and E. Witten, Vector bundles over elliptic fibrations, alg-geom/9709029 [INSPIRE].
M. Bershadsky, T.M. Chiang, B.R. Greene, A. Johansen and C.I. Lazaroiu, F-theory and linear σ-models, Nucl. Phys. B 527 (1998) 531 [hep-th/9712023] [INSPIRE].
P.S. Aspinwall and R.Y. Donagi, The heterotic string, the tangent bundle and derived categories, Adv. Theor. Math. Phys. 2 (1998) 1041 [hep-th/9806094] [INSPIRE].
R. Donagi and M. Wijnholt, Gluing branes II: flavour physics and string duality, JHEP 05 (2013) 092 [arXiv:1112.4854] [INSPIRE].
F. Rohsiepe, Fibration structures in toric Calabi-Yau fourfolds, hep-th/0502138 [INSPIRE].
P. Candelas, A. Constantin and H. Skarke, An abundance of K3 fibrations from polyhedra with interchangeable parts, Commun. Math. Phys. 324 (2013) 937 [arXiv:1207.4792] [INSPIRE].
S.B. Johnson and W. Taylor, Calabi-Yau threefolds with large h 2,1, JHEP 10 (2014) 023 [arXiv:1406.0514] [INSPIRE].
J. Gray, A.S. Haupt and A. Lukas, Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds, JHEP 09 (2014) 093 [arXiv:1405.2073] [INSPIRE].
S.B. Johnson and W. Taylor, Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds, Fortsch. Phys. 64 (2016) 581 [arXiv:1605.08052] [INSPIRE].
L.B. Anderson, X. Gao, J. Gray and S.-J. Lee, Multiple fibrations in Calabi-Yau geometry and string dualities, JHEP 10 (2016) 105 [arXiv:1608.07555] [INSPIRE].
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ArXiv ePrint: 1611.10291
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García-Etxebarria, I., Lüst, D., Massai, S. et al. Ubiquity of non-geometry in heterotic compactifications. J. High Energ. Phys. 2017, 46 (2017). https://doi.org/10.1007/JHEP03(2017)046
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DOI: https://doi.org/10.1007/JHEP03(2017)046