×

zbMATH — the first resource for mathematics

New Higgs transitions between dual \(N=2\) string models. (English) Zbl 0925.14012
Summary: We describe a new kind of transition between topologically distinct \(N=2\) type II Calabi-Yau vacua through points with enhanced non-abelian gauge symmetries together with fundamental charged matter hyper multiplets. We connect the appearance of matter to the local geometry of the singularity and discuss the relation between the instanton numbers of the Calabi-Yau manifolds taking part in the transition. In a dual heterotic string theory on \(K3\times T^2\) the process corresponds to Higgsing a semi-classical gauge group or equivalently to a variation of the gauge bundle. In special cases the situation reduces to simple conifold transitions in the Coulomb phase of the non-abelian gauge symmetries.

MSC:
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32J81 Applications of compact analytic spaces to the sciences
83E30 String and superstring theories in gravitational theory
Software:
schubert
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Witten, E., Nucl. phys. B, 443, 85, (1995), hep-th/9503124
[2] Seiberg, N.; Witten, E., Nucl. phys. B, 426, 19, (1994), hep-th/9407087
[3] Klemm, A.; Lerche, W.; Theisen, S.; Yankielowicz, S.; Argyres, P.; Faraggi, A.; Danielsson, Ulf H.; Sundborg, Bo; Brandhuber, A.; Landsteiner, K.; Leigh, R.G.; Strassler, M.J.; Martinec, E.; Warner, N., Phys. lett. B, Phys. rev. lett., Phys. lett. B, Phys. lett. B, Phys. lett. B, Nucl. phys. B, 459, 97, (1996)
[4] Hull, C.; Townsend, P., Nucl. phys. B, 438, 109, (1995), hep-th 9410167
[5] Kachru, S.; Vafa, C., Nucl. phys. B, 450, 69, (1995), hep-th/9505105
[6] Ferrara, S.; Harvey, J.; Strominger, A.; Vafa, C., Phys. lett. B, 361, 59, (1995), hep-th/9505162
[7] de Wit, B.; Lauwers, P.G.; Philippe, R.; Su, S.Q.; van Proeyen, A.; de Wit, B.; van Proeyen, A.; Derendinger, J.P.; Ferrara, S.; Masiero, A.; van Proeyen, A.; de Wit, B.; Lauwers, P.G.; van Proeyen, A.; Cremmer, E.; Kounnas, C.; van Proeyen, A.; Derendinger, J.P.; Ferrara, S.; de Wit, B.; Girardello, L., Phys. lett. B, Nucl. phys. B, Phys. lett. B, Nucl. phys. B, Nucl. phys. B, 250, 385, (1985)
[8] Bagger, J.; Witten, E.; Bagger, J.; Galperin, A.; Ivanov, E.; Ogievetsky, V., Nucl. phys. B, Nucl. phys. B, 303, 522, (1988)
[9] de Wit, B.; Kaplunovsky, V.; Louis, J.; Lüst, D.; Antoniadis, I.; Ferrara, S.; Gava, E.; Narain, K.S.; Taylor, T.R., Nucl. phys. B, Nucl. phys. B, 447, 35, (1995)
[10] Kaplunovsky, V.; Louis, J.; Theisen, S.; Klemm, A.; Lerche, W.; Mayr, P., Phys. lett. B, Phys. lett. B, 357, 313, (1995)
[11] C. Vafa and E. Witten, preprint HUTP-95-A023; hep-th/9507050
[12] B. Lian and S.T. Yau, Mirror Maps, Modular Relations and Hypergeometric Series I,II, hep-th/9507151, hep-th 9507153; G. Lopes Cardoso, G. Curio, D. Lüst and T. Mohaupt, Instanton Numbers and Exchange Symmetries in N = 2 Dual String Pairs, hep-th/9603108.
[13] Kachru, S.; Klemm, A.; Lerche, W.; Mayr, P.; Vafa, C., Nucl. phys. B, 459, 537, (1996)
[14] Aspinwall, P.; Aspinwall, P., Phys. lett. B, Phys. lett. B, 371, 231, (1996), hep-th/9511171
[15] T. Chiang, B.R. Greene, M. Gross and Y. Kanter, Black hole condensation and the web of Calabi-Yau manifolds, hep-th 9511204.
[16] Aldazabal, G.; Ibáñez, L.E.; Font, A.; Quevedo, F., Nucl. phys. B, 461, 85, (1996), hep-th/9510093
[17] P. Candelas and A. Font, Duality Between Webs of Heterotic and Type II Vacua, hep-th/9603170, Nucl. Phys. B, to be published. · Zbl 0947.81054
[18] Katz, S.; Morrison, D.R.; Plesser, M.R., Nucl. phys. B, 477, 105, (1996), hep-th/9601108
[19] Strominger, A., Nucl. phys. B, 451, 96, (1995), hep-th/9504090
[20] Bershadsky, M.; Sadov, V.; Vafa, C., Nucl. phys. B, 463, 398, (1996), hep-th/9510225
[21] Klemm, A.; Mayr, P., Nucl. phys. B, 469, 37, (1996), hep-th/9601014
[22] Klemm, A.; Lerche, W.; Mayr, P.; Vafa, C.; Warner, N., Nucl. phys. B, 477, 746, (1996), hep-th/9604034
[23] D.R. Morrison and M.R. Plesser, private communication.
[24] Miranda, R., (), 85
[25] Harris, J., Algebraic geomtry, (1992), Springer Berlin
[26] Aspinwall, P.; Greene, B.; Morrison, D., Nucl. phys. B, 420, 184, (1994)
[27] Berglund, P.; Katz, S.; Klemm, A., Nucl. phys. B, 456, 153, (1995), hep-th/9506091
[28] D.R. Morrison, Through the looking glass, to appear. · Zbl 0935.32020
[29] Oguiso, K., Int. J. math., 4, 439, (1993)
[30] Hunt, B.; Schimmrigk, R., Phys. lett. B, 381, 427, (1996), hep-th/9512138
[31] P. Berglund, S. Katz, A. Klemm and P. Mayr, Type II Strings on Calabi-Yau Manifolds and String Duality, in preparation.
[32] Aldazabal, G.; Font, A.; Ibáñez, L.E.; Quevedo, F., Phys. lett. B, 380, 33, (1996), hep-th/9602097
[33] Batyrev, V.; Batyrev, V., Quantum cohomology rings of toric manifolds, Duke math. J., J. alg. geom., 3, 493, (1992), preprint · Zbl 0829.14023
[34] S. Hosono, B.H. Lian, S.-T. Yau, GKZ Hypergeometric Systems and Applications to Mirror Symmetry, alg-geom/9511001. · Zbl 0870.14028
[35] J. DeLoera, PUNTOS, ftp.geom.umn.edu/pub/software.
[36] Aspinwall, P., Nucl. phys. B, 460, 57, (1996), hep-th/9510142
[37] D.R. Morrison, hep-th 9311049
[38] Hosono, S.; Klemm, A.; Theisen, S.; Yau, S.-T.; Hosono, S.; Klemm, A.; Theisen, S.; Yau, S.-T., Commun. math. phys., Nucl. phys. B, 433, 501, (1995)
[39] Klemm, A.; Lerche, W.; Mayr, P., Phys. lett. B, 357, 71, (1995)
[40] S. Katz and S.A. Strømme, Schubert: a Maple package for intersection theory, ftp.math.okstate.edu/pub/schubert.
[41] Candelas, P.; de la Ossa, X.; Font, A.; Katz, S.; Morrison, D., Nucl. phys. B, 416, 481, (1994), hep-th/9308083
[42] Morrison, D.R.; Vafa, C., Nucl. phys. B, 473, 74, (1996), hep-th/96002114
[43] Aspinwall, P.S.; Gross, Mark, Phys. lett. B, 382, 81, (1996), hep-th/9602118
[44] M. Gross, Primitive Calabi-Yau Threefolds, alg-geom/9512002.
[45] Mayr, P.; Stieberger, S.; Lopes Cardoso, G.; Lüst, D.; Mohaupt, T., Phys. lett. B, Nucl. phys. B, 432, 68, (1994)
[46] Greene, B.R.; Morrison, D.R.; Strominger, A., Nucl. phys. B, 451, 109, (1996), hep-th/9504145
[47] P.S. Aspinwall and M. Gross, The SO(32) Heterotic String on a K3 Surface, hep-th/9605131, Phys. Lett. B, to be published.
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.