zbMATH — the first resource for mathematics

Global F-theory models: instantons and gauge dynamics. (English) Zbl 1214.81149
Summary: We present and analyze in detail a compact F-theory GUT model in which D-brane instantons generate the top Yukawa coupling non-perturbatively. We elucidate certain aspects of F-theory gauge dynamics which are absent in the Type IIB limit, due to quantum splitting of certain brane stacks. Finally, we provide a working implementation of an algorithm for computing cohomology of line bundles on arbitrary toric varieties. This should be of general use for studying the physics of global Type IIB and F-theory models, in particular for the explicit counting of zero modes for rigid F-theory instantons which contribute to charged matter couplings.

81T13 Yang-Mills and other gauge theories in quantum field theory
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
81V22 Unified quantum theories
81V17 Gravitational interaction in quantum theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)
Full Text: DOI arXiv
[1] Vafa, C., Evidence for F-theory, Nucl. Phys., B 469, 403, (1996)
[2] Blumenhagen, R.; Cvetič, M.; Langacker, P.; Shiu, G., Toward realistic intersecting D-brane models, Ann. Rev. Nucl. Part. Sci., 55, 71, (2005)
[3] Blumenhagen, R.; Körs, B.; Lüst, D.; Stieberger, S., Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rept., 445, 1, (2007)
[4] Cvetič, M.; Halverson, J.; Richter, R., Realistic Yukawa structures from orientifold compactifications, JHEP, 12, 063, (2009)
[5] Cvetič, M.; Halverson, J.; Richter, R., Mass hierarchies from MSSM orientifold compactifications, JHEP, 07, 005, (2010)
[6] M. Cvetič, J. Halverson and R. Richter, Mass Hierarchies vs. Proton Decay in MSSM Orientifold Compactifications, arXiv:0910.2239 [SPIRES].
[7] Cvetič, M.; Halverson, J.; Langacker, P.; Richter, R., The Weinberg operator and a lower string scale in orientifold compactifications, JHEP, 10, 094, (2010)
[8] R. Donagi and M. Wijnholt, Model Building with F-theory, arXiv:0802.2969 [SPIRES].
[9] Beasley, C.; Heckman, JJ; Vafa, C., GUTs and exceptional branes in F-theory — I, JHEP, 01, 058, (2009)
[10] Beasley, C.; Heckman, JJ; Vafa, C., GUTs and exceptional branes in F-theory — II: experimental predictions, JHEP, 01, 059, (2009)
[11] R. Donagi and M. Wijnholt, Breaking GUT Groups in F-theory, arXiv:0808.2223 [SPIRES].
[12] Witten, E., Non-perturbative superpotentials in string theory, Nucl. Phys., B 474, 343, (1996)
[13] Balasubramanian, V.; Berglund, P.; Conlon, JP; Quevedo, F., Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP, 03, 007, (2005)
[14] Denef, F.; Douglas, MR; Florea, B., Building a better racetrack, JHEP, 06, 034, (2004)
[15] Kachru, S.; Kallosh, R.; Linde, AD; Trivedi, SP, De Sitter vacua in string theory, Phys. Rev., D 68, 046005, (2003)
[16] Ganor, OJ, On zeroes of superpotentials in F-theory, Nucl. Phys. Proc. Suppl., 67, 25, (1998)
[17] Blumenhagen, R.; Cvetič, M.; Weigand, T., Spacetime instanton corrections in 4D string vacua — the seesaw mechanism for D-brane models, Nucl. Phys., B 771, 113, (2007)
[18] Ibáñez, LE; Uranga, AM, Neutrino Majorana masses from string theory instanton effects, JHEP, 03, 052, (2007)
[19] Florea, B.; Kachru, S.; McGreevy, J.; Saulina, N., Stringy instantons and quiver gauge theories, JHEP, 05, 024, (2007)
[20] Blumenhagen, R.; Cvetič, M.; Kachru, S.; Weigand, T., D-brane instantons in type II orientifolds, Ann. Rev. Nucl. Part. Sci., 59, 269, (2009)
[21] Blumenhagen, R.; Collinucci, A.; Jurke, B., On instanton effects in F-theory, JHEP, 08, 079, (2010)
[22] J.J. Heckman, J. Marsano, N. Saulina, S. Schäfer-Nameki and C. Vafa, Instantons and SUSY breaking in F-theory, arXiv:0808.1286 [SPIRES].
[23] Marsano, J.; Saulina, N.; Schäfer-Nameki, S., An instanton toolbox for F-theory model building, JHEP, 01, 128, (2010)
[24] Cvetič, M.; Garcia-Etxebarria, I.; Richter, R., Branes and instantons intersecting at angles, JHEP, 01, 005, (2010)
[25] Cvetič, M.; Garcia-Etxebarria, I.; Richter, R., Branes and instantons at angles and the F-theory lift of \(O\)(1) instantons, AIP Conf. Proc., 1200, 246, (2010)
[26] H. Skarke, String dualities and toric geometry: An introduction, hep-th/9806059 [SPIRES].
[27] C. Closset, Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists), arXiv:0901.3695 [SPIRES].
[28] V. Bouchard, Lectures on complex geometry, Calabi-Yau manifolds and toric geometry, hep-th/0702063 [SPIRES].
[29] D. Cox, Lectures on toric varieties, http://www.cs.amherst.edu/∼dac/lectures/coxcimpa.pdf.
[30] D. Cox, J. Little and H. Schenck, Toric varieties, to appear in Amer. Math. Soc.http://www.cs.amherst.edu/∼dac/toric.html.
[31] W. Fulton, Introduction to toric varieties, Princeton University Press, Princeton U.S.A. (1993), pg. 157.
[32] Blumenhagen, R.; Jurke, B.; Rahn, T.; Roschy, H., Cohomology of line bundles: A computational algorithm, J. Math. Phys., 51, 103525, (2010)
[33] Blumenhagen, R.; Braun, V.; Grimm, TW; Weigand, T., GUTs in type IIB orientifold compactifications, Nucl. Phys., B 815, 1, (2009)
[34] Collinucci, A., New F-theory lifts, JHEP, 08, 076, (2009)
[35] Collinucci, A., New F-theory lifts II: permutation orientifolds and enhanced singularities, JHEP, 04, 076, (2010)
[36] Blumenhagen, R.; Grimm, TW; Jurke, B.; Weigand, T., F-theory uplifts and guts, JHEP, 09, 053, (2009)
[37] Marsano, J.; Saulina, N.; Schäfer-Nameki, S., F-theory compactifications for supersymmetric guts, JHEP, 08, 030, (2009)
[38] Marsano, J.; Saulina, N.; Schäfer-Nameki, S., Monodromies, fluxes and compact three-generation F-theory guts, JHEP, 08, 046, (2009)
[39] Blumenhagen, R.; Grimm, TW; Jurke, B.; Weigand, T., Global F-theory guts, Nucl. Phys. B, 829, 325, (2010)
[40] Marsano, J.; Saulina, N.; Schäfer-Nameki, S., Compact F-theory GUTs with \(U\)(1)_{PQ}, JHEP, 04, 095, (2010)
[41] Grimm, TW; Krause, S.; Weigand, T., F-theory GUT vacua on compact Calabi-Yau fourfolds, JHEP, 07, 037, (2010)
[42] Tate, J., Algorithm for determining the type of a singular fiber in an elliptic pencil, (1972), Antwerp Belgium
[43] Bershadsky, M.; etal., Geometric singularities and enhanced gauge symmetries, Nucl. Phys., B 481, 215, (1996)
[44] Sen, A., Orientifold limit of F-theory vacua, Phys. Rev., D 55, 7345, (1997)
[45] Sen, A., F-theory and the gimon-polchinski orientifold, Nucl. Phys., B 498, 135, (1997)
[46] Banks, T.; Douglas, MR; Seiberg, N., Probing F-theory with branes, Phys. Lett., B 387, 278, (1996)
[47] Seiberg, N.; Witten, E., Monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys., B 426, 19, (1994)
[48] Seiberg, N.; Witten, E., Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys., B 431, 484, (1994)
[49] Gaberdiel, MR; Zwiebach, B., Exceptional groups from open strings, Nucl. Phys., B 518, 151, (1998)
[50] DeWolfe, O.; Zwiebach, B., String junctions for arbitrary Lie algebra representations, Nucl. Phys., B 541, 509, (1999)
[51] Argurio, R.; Bertolini, M.; Franco, S.; Kachru, S., Metastable vacua and D-branes at the conifold, JHEP, 06, 017, (2007)
[52] Argurio, R.; Bertolini, M.; Ferretti, G.; Lerda, A.; Petersson, C., Stringy instantons at orbifold singularities, JHEP, 06, 067, (2007)
[53] Bianchi, M.; Fucito, F.; Morales, JF, D-brane instantons on the \(T\)\^{}{6}/\(Z\)_{3} orientifold, JHEP, 07, 038, (2007)
[54] Ibáñez, LE; Schellekens, AN; Uranga, AM, Instanton induced neutrino Majorana masses in CFT orientifolds with MSSM-like spectra, JHEP, 06, 011, (2007)
[55] W. Stein et al., Sage Mathematics Software (Version 4.3.4), The Sage Development Team, 2010, http://www.sagemath.org.
[56] The CHomP Group, http://chomp.rutgers.edu.
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.