×

zbMATH — the first resource for mathematics

On instanton effects in F-theory. (English) Zbl 1290.81103
Summary: We revisit the issue of M5-brane instanton corrections to the superpotential in F-theory compactifications on elliptically fibered Calabi-Yau fourfolds. Elaborating on concrete geometries, we compare the instanton zero modes for non-perturbative F-theory models with the zero modes in their perturbative Sen limit. The fermionic matter zero modes localized on the intersection of the instanton with the space-time filling D7-branes show up in a geometric way in F-theory. Methods for their computation are developed and, not surprisingly, exceptional gauge group structures do appear. Finally, quite intriguing geometrical aspects of the one-loop determinant are discussed.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory
20G41 Exceptional groups
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] R. Donagi and M. Wijnholt, Model building with F-theory, arXiv:0802.2969 [SPIRES].
[2] Beasley, C.; Heckman, JJ; Vafa, C., GUTs and exceptional branes in F-theory — I, JHEP, 01, 058, (2009)
[3] Beasley, C.; Heckman, JJ; Vafa, C., GUTs and exceptional branes in F-theory — II: experimental predictions, JHEP, 01, 059, (2009)
[4] R. Donagi and M. Wijnholt, Breaking GUT groups in F-theory, arXiv:0808.2223 [SPIRES].
[5] Hayashi, H.; Kawano, T.; Tatar, R.; Watari, T., Codimension-3 singularities and Yukawa couplings in F-theory, Nucl. Phys., B 823, 47, (2009)
[6] Andreas, B.; Curio, G., From local to global in F-theory model building, J. Geom. Phys., 60, 1089, (2010)
[7] R. Donagi and M. Wijnholt, Higgs bundles and UV completion in F-theory, arXiv:0904.1218 [SPIRES].
[8] Marsano, J.; Saulina, N.; Schäfer-Nameki, S., F-theory compactifications for supersymmetric guts, JHEP, 08, 030, (2009)
[9] Blumenhagen, R.; Grimm, TW; Jurke, B.; Weigand, T., Global F-theory guts, Nucl. Phys., B 829, 325, (2010)
[10] Grimm, TW; Krause, S.; Weigand, T., F-theory GUT vacua on compact Calabi-Yau fourfolds, JHEP, 07, 037, (2010)
[11] F. Denef, Les Houches lectures on constructing string vacua, arXiv:0803.1194 [SPIRES].
[12] J.J. Heckman, Particle physics implications of F-theory, arXiv:1001.0577 [SPIRES].
[13] Blumenhagen, R.; Körs, B.; Lüst, D.; Ott, T., The standard model from stable intersecting brane world orbifolds, Nucl. Phys., B 616, 3, (2001)
[14] Blumenhagen, R.; Cvetič, M.; Lüst, D.; Richter, R.; Weigand, T., Non-perturbative Yukawa couplings from string instantons, Phys. Rev. Lett., 100, 061602, (2008)
[15] 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)
[16] Ibáñez, LE; Uranga, AM, Neutrino Majorana masses from string theory instanton effects, JHEP, 03, 052, (2007)
[17] Argurio, R.; Bertolini, M.; Ferretti, G.; Lerda, A.; Petersson, C., Stringy instantons at orbifold singularities, JHEP, 06, 067, (2007)
[18] Ibáñez, LE; Schellekens, AN; Uranga, AM, Instanton induced neutrino Majorana masses in CFT orientifolds with MSSM-like spectra, JHEP, 06, 011, (2007)
[19] Blumenhagen, R.; Cvetič, M.; Kachru, S.; Weigand, T., D-brane instantons in type II orientifolds, Ann. Rev. Nucl. Part. Sci., 59, 269, (2009)
[20] Kachru, S.; Kallosh, R.; Linde, AD; Trivedi, SP, De Sitter vacua in string theory, Phys. Rev., D 68, 046005, (2003)
[21] Balasubramanian, V.; Berglund, P.; Conlon, JP; Quevedo, F., Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP, 03, 007, (2005)
[22] M. Alim et al., Hints for off-shell mirror symmetry in type-II/F-theory compactifications, arXiv:0909.1842 [SPIRES].
[23] Grimm, TW; Ha, T-W; Klemm, A.; Klevers, D., Computing brane and flux superpotentials in F-theory compactifications, JHEP, 04, 015, (2010)
[24] Grimm, TW; Ha, T-W; Klemm, A.; Klevers, D., Five-brane superpotentials and heterotic/F-theory duality, Nucl. Phys., B 838, 458, (2010)
[25] Witten, E., Non-perturbative superpotentials in string theory, Nucl. Phys., B 474, 343, (1996)
[26] Becker, K.; Becker, M.; Strominger, A., Five-branes, membranes and nonperturbative string theory, Nucl. Phys., B 456, 130, (1995)
[27] Robbins, D.; Sethi, S., A barren landscape, Phys. Rev., D 71, 046008, (2005)
[28] J.J. Heckman, J. Marsano, N. Saulina, S. Schäfer-Nameki and C. Vafa, Instantons and SUSY breaking in F-theory, arXiv:0808.1286 [SPIRES].
[29] Marsano, J.; Saulina, N.; Schäfer-Nameki, S., An instanton toolbox for F-theory model building, JHEP, 01, 128, (2010)
[30] Cvetič, M.; Garcia-Etxebarria, I.; Richter, R., Branes and instantons intersecting at angles, JHEP, 01, 005, (2010)
[31] 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)
[32] P. Berglund and P. Mayr, Non-perturbative superpotentials in F-theory and string duality, hep-th/0504058 [SPIRES].
[33] H. Jockers, P. Mayr and J. Walcher, On N = 14D effective couplings for F-theory and heterotic vacua, arXiv:0912.3265 [SPIRES].
[34] Collinucci, A., New F-theory lifts, JHEP, 08, 076, (2009)
[35] Blumenhagen, R.; Grimm, TW; Jurke, B.; Weigand, T., F-theory uplifts and guts, JHEP, 09, 053, (2009)
[36] Collinucci, A., New F-theory lifts II: permutation orientifolds and enhanced singularities, JHEP, 04, 076, (2010)
[37] Kallosh, R.; Kashani-Poor, A-K; Tomasiello, A., Counting fermionic zero modes on M5 with fluxes, JHEP, 06, 069, (2005)
[38] Bergshoeff, E.; Kallosh, R.; Kashani-Poor, A-K; Sorokin, D.; Tomasiello, A., An index for the Dirac operator on D3 branes with background fluxes, JHEP, 10, 102, (2005)
[39] Park, J., D3 instantons in Calabi-Yau orientifolds with(out) fluxes, Eur. Phys. J., C 67, 263, (2010)
[40] Blumenhagen, R.; Cvetič, M.; Richter, R.; Weigand, T., Lifting D-instanton zero modes by recombination and background fluxes, JHEP, 10, 098, (2007)
[41] Witten, E., Five-brane effective action in M-theory, J. Geom. Phys., 22, 103, (1997)
[42] Blumenhagen, R.; Braun, V.; Grimm, TW; Weigand, T., GUTs in type IIB orientifold compactifications, Nucl. Phys., B 815, 1, (2009)
[43] Argurio, R.; Bertolini, M.; Franco, S.; Kachru, S., Metastable vacua and D-branes at the conifold, JHEP, 06, 017, (2007)
[44] Collinucci, A.; Denef, F.; Esole, M., D-brane deconstructions in IIB orientifolds, JHEP, 02, 005, (2009)
[45] Sen, A., F-theory and orientifolds, Nucl. Phys., B 475, 562, (1996)
[46] Sen, A., Orientifold limit of F-theory vacua, Phys. Rev., D 55, 7345, (1997)
[47] Douglas, MR; Taylor, W., The landscape of intersecting brane models, JHEP, 01, 031, (2007)
[48] Blumenhagen, R.; Moster, S.; Reinbacher, R.; Weigand, T., Massless spectra of three generation U(\(N\)) heterotic string vacua, JHEP, 05, 041, (2007)
[49] Distler, J.; Greene, BR; Morrison, DR, Resolving singularities in (0, 2) models, Nucl. Phys., B 481, 289, (1996)
[50] Blumenhagen, R., Target space duality for (0, 2) compactifications, Nucl. Phys., B 513, 573, (1998)
[51] Bershadsky, M.; etal., Geometric singularities and enhanced gauge symmetries, Nucl. Phys., B 481, 215, (1996)
[52] Friedman, R.; Morgan, J.; Witten, E., Vector bundles and F-theory, Commun. Math. Phys., 187, 679, (1997)
[53] Distler, J.; Greene, BR, A spects of (2, 0) string compactifications, Nucl. Phys., B 304, 1, (1988)
[54] Buchbinder, EI; Donagi, R.; Ovrut, BA, Superpotentials for vector bundle moduli, Nucl. Phys., B 653, 400, (2003)
[55] Curio, G., Perspectives on pfaffians of heterotic world-sheet instantons, JHEP, 09, 131, (2009)
[56] Gaberdiel, MR; Zwiebach, B., Tensor constructions of open string theories. II: vector bundles, D-branes and orientifold groups, Phys. Lett., B 410, 151, (1997)
[57] Aluffi, P.; Esole, M., New orientifold weak coupling limits in F-theory, JHEP, 02, 020, (2010)
[58] Diaconescu, D-E; Gukov, S., Three dimensional N = 2 gauge theories and degenerations of Calabi-Yau four-folds, Nucl. Phys., B 535, 171, (1998)
[59] Braun, AP; Gerigk, S.; Hebecker, A.; Triendl, H., D7-brane moduli vs. F-theory cycles in elliptically fibred threefolds, Nucl. Phys., B 836, 1, (2010)
[60] Tripathy, PK; Trivedi, SP, D3 brane action and fermion zero modes in presence of background flux, JHEP, 06, 066, (2005)
[61] Saulina, N., Topological constraints on stabilized flux vacua, Nucl. Phys., B 720, 203, (2005)
[62] Tsimpis, D., Fivebrane instantons and Calabi-Yau fourfolds with flux, JHEP, 03, 099, (2007)
[63] Brunner, I.; Hori, K., Orientifolds and mirror symmetry, JHEP, 11, 005, (2004)
[64] Distler, J.; Greene, BR, Some exact results on the superpotential from Calabi-Yau compactifications, Nucl. Phys., B 309, 295, (1988)
[65] Bershadsky, M.; Chiang, TM; Greene, BR; Johansen, A.; Lazaroiu, CI, F-theory and linear σ-models, Nucl. Phys., B 527, 531, (1998)
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.