Special points of inflation in flux compactifications. (English) Zbl 1331.81236
Summary: We study the realization of axion inflation models in the complex structure moduli spaces of Calabi-Yau threefolds and fourfolds. The axions arise close to special points of these moduli spaces that admit discrete monodromy symmetries of infinite order. Examples include the large complex structure point and conifold point, but can be of more general nature. In Type IIB and F-theory compactifications the geometric axions receive a scalar potential from a flux-induced superpotential. We find toy variants of various inflationary potentials including the ones for natural inflation of one or multiple axions, or axion monodromy inflation with polynomial potential. Interesting examples are also given by mirror geometries of torus fibrations with Mordell-Weil group of rank \(N - 1\) or an \(N\)-section, which admit an axion if \(N > 3\).
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 81V05 | Strong interaction, including quantum chromodynamics |
| 14D21 | Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 83F05 | Relativistic cosmology |
Software:
DLMFReferences:
| [1] | Baumann, D.; McAllister, L., Inflation and string theory · Zbl 1339.83003 |
| [2] | Douglas, M. R.; Kachru, S., Flux compactification, Rev. Mod. Phys., 79, 733-796 (2007) · Zbl 1205.81011 |
| [3] | Blumenhagen, R.; Kors, B.; Lust, D.; Stieberger, S., Four-dimensional string compactifications with D-branes, orientifolds and fluxes, Phys. Rep., 445, 1-193 (2007) |
| [4] | Ade, P., Detection of B-mode polarization at degree angular scales by BICEP2, Phys. Rev. Lett., 112, Article 241101 pp. (2014) |
| [5] | Adam, R., Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes |
| [6] | Kim, J. E.; Nilles, H. P.; Peloso, M., Completing natural inflation, J. Cosmol. Astropart. Phys., 0501, Article 005 pp. (2005) |
| [7] | Kappl, R.; Krippendorf, S.; Nilles, H. P., Aligned natural inflation: monodromies of two axions, Phys. Lett. B, 737, 124-128 (2014) · Zbl 1317.83107 |
| [8] | Long, C.; McAllister, L.; McGuirk, P., Aligned natural inflation in string theory, Phys. Rev. D, 90, Article 023501 pp. (2014) |
| [9] | Gao, X.; Li, T.; Shukla, P., Combining universal and odd RR axions for aligned natural inflation, J. Cosmol. Astropart. Phys., 1410, 10, Article 048 pp. (2014) |
| [10] | Liddle, A. R.; Mazumdar, A.; Schunck, F. E., Assisted inflation, Phys. Rev. D, 58, Article 061301 pp. (1998) |
| [11] | Dimopoulos, S.; Kachru, S.; McGreevy, J.; Wacker, J. G., N-flation, J. Cosmol. Astropart. Phys., 0808, Article 003 pp. (2008) |
| [12] | Grimm, T. W., Axion inflation in type II string theory, Phys. Rev. D, 77, Article 126007 pp. (2008) |
| [13] | Cicoli, M.; Dutta, K.; Maharana, A., N-flation with hierarchically light axions in string compactifications, J. Cosmol. Astropart. Phys., 1408, Article 012 pp. (2014) |
| [14] | Bachlechner, T. C.; Dias, M.; Frazer, J.; McAllister, L., A new angle on chaotic inflation |
| [15] | Silverstein, E.; Westphal, A., Monodromy in the CMB: gravity waves and string inflation, Phys. Rev. D, 78, Article 106003 pp. (2008) |
| [16] | McAllister, L.; Silverstein, E.; Westphal, A., Gravity waves and linear inflation from axion monodromy, Phys. Rev. D, 82, Article 046003 pp. (2010) |
| [17] | Kaloper, N.; Sorbo, L., A natural framework for chaotic inflation, Phys. Rev. Lett., 102, Article 121301 pp. (2009) |
| [18] | Palti, E.; Weigand, T., Towards large \(r\) from \([p, q]\)-inflation, J. High Energy Phys., 1404, Article 155 pp. (2014) |
| [19] | Marchesano, F.; Shiu, G.; Uranga, A. M., F-term axion monodromy inflation, J. High Energy Phys., 1409, Article 184 pp. (2014) |
| [20] | Hebecker, A.; Kraus, S. C.; Witkowski, L. T., D7-brane chaotic inflation, Phys. Lett. B, 737, 16-22 (2014) · Zbl 1317.83089 |
| [21] | Blumenhagen, R.; Plauschinn, E., Towards universal axion inflation and reheating in string theory, Phys. Lett. B, 736, 482-487 (2014) · Zbl 1317.83087 |
| [22] | Ibanez, L. E.; Valenzuela, I., The inflaton as an MSSM Higgs and open string modulus monodromy inflation, Phys. Lett. B, 736, 226-230 (2014) |
| [23] | Arends, M.; Hebecker, A.; Heimpel, K.; Kraus, S. C.; Lust, D., D7-brane moduli space in axion monodromy and fluxbrane inflation, Fortschr. Phys., 62, 647-702 (2014) · Zbl 1338.83182 |
| [24] | McAllister, L.; Silverstein, E.; Westphal, A.; Wrase, T., The powers of monodromy, J. High Energy Phys., 1409, Article 123 pp. (2014) |
| [25] | Franco, S.; Galloni, D.; Retolaza, A.; Uranga, A., Axion monodromy inflation on warped throats · Zbl 1388.83912 |
| [26] | Ibanez, L. E.; Marchesano, F.; Valenzuela, I., Higgs-otic inflation and string theory · Zbl 1388.83668 |
| [27] | Grimm, T. W., The effective action of type II Calabi-Yau orientifolds, Fortschr. Phys., 53, 1179-1271 (2005) · Zbl 1075.81052 |
| [28] | Vafa, C., Evidence for F theory, Nucl. Phys. B, 469, 403-418 (1996) · Zbl 1003.81531 |
| [29] | Denef, F., Les Houches lectures on constructing string vacua |
| [30] | Blumenhagen, R.; Herschmann, D.; Plauschinn, E., The challenge of realizing F-term axion monodromy inflation in string theory · Zbl 1390.83375 |
| [31] | Hayashi, H.; Matsuda, R.; Watari, T., Issues in complex structure moduli inflation |
| [32] | Hebecker, A.; Mangat, P.; Rompineve, F.; Witkowski, L. T., Tuning and backreaction in F-term axion monodromy inflation · Zbl 1328.83197 |
| [33] | Gukov, S.; Vafa, C.; Witten, E., CFT’s from Calabi-Yau four folds, Nucl. Phys. B, 584, 69-108 (2000) · Zbl 0984.81143 |
| [34] | Giddings, S. B.; Kachru, S.; Polchinski, J., Hierarchies from fluxes in string compactifications, Phys. Rev. D, 66, Article 106006 pp. (2002) |
| [35] | Cox, D.; Katz, S., Mirror Symmetry and Algebraic Geometry, Mathematical Surveys and Monographs, vol. 68 (1999), AMS · Zbl 0951.14026 |
| [36] | Hori, K.; Katz, S.; Klemm, A.; Pandharipande, R.; Thomas, R., Mirror Symmetry, Clay Mathematics Monographs, vol. 1 (2003), AMS · Zbl 1044.14018 |
| [37] | Aspinwall, P. S., D-branes on Calabi-Yau manifolds · Zbl 1084.81058 |
| [38] | Berglund, P.; Candelas, P.; De La Ossa, X.; Font, A.; Hubsch, T., Periods for Calabi-Yau and Landau-Ginzburg vacua, Nucl. Phys. B, 419, 352-403 (1994) · Zbl 0896.14022 |
| [39] | Hosono, S.; Klemm, A.; Theisen, S.; Yau, S.-T., Mirror symmetry, mirror map and applications to Calabi-Yau hypersurfaces, Commun. Math. Phys., 167, 301-350 (1995) · Zbl 0814.53056 |
| [40] | Hosono, S.; Klemm, A.; Theisen, S.; Yau, S.-T., Mirror symmetry, mirror map and applications to complete intersection Calabi-Yau spaces, Nucl. Phys. B, 433, 501-554 (1995) · Zbl 0908.32008 |
| [41] | Greene, B. R.; Lazaroiu, C., Collapsing D-branes in Calabi-Yau moduli space. 1, Nucl. Phys. B, 604, 181-255 (2001) · Zbl 0983.81075 |
| [42] | Mayr, P., Phases of supersymmetric D-branes on Kahler manifolds and the McKay correspondence, J. High Energy Phys., 0101, Article 018 pp. (2001) |
| [43] | Grimm, T. W.; Louis, J., The effective action of \(N = 1\) Calabi-Yau orientifolds, Nucl. Phys. B, 699, 387-426 (2004) · Zbl 1123.81393 |
| [44] | Benini, F.; Cremonesi, S., Partition functions of \(N = (2, 2)\) gauge theories on \(S^2\) and vortices · Zbl 1308.81131 |
| [45] | Doroud, N.; Gomis, J.; Le Floch, B.; Lee, S., Exact results in \(D = 2\) supersymmetric gauge theories, J. High Energy Phys., 1305, Article 093 pp. (2013) · Zbl 1342.81573 |
| [46] | Jockers, H.; Kumar, V.; Lapan, J. M.; Morrison, D. R.; Romo, M., Two-sphere partition functions and Gromov-Witten invariants, Commun. Math. Phys., 325, 1139-1170 (2014) · Zbl 1301.81253 |
| [47] | Halverson, J.; Jockers, H.; Lapan, J. M.; Morrison, D. R., Perturbative corrections to Kahler moduli spaces · Zbl 1427.32011 |
| [48] | Hori, K.; Romo, M., Exact results in two-dimensional \((2, 2)\) supersymmetric gauge theories with boundary |
| [49] | Kim, H.; Lee, S.; Yi, P., Exact partition functions on \(RP^2\) and orientifolds, J. High Energy Phys., 1402, Article 103 pp. (2014) |
| [50] | Freese, K.; Frieman, J. A.; Olinto, A. V., Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett., 65, 3233-3236 (1990) |
| [51] | Adams, F. C.; Bond, J. R.; Freese, K.; Frieman, J. A.; Olinto, A. V., Natural inflation: particle physics models, power law spectra for large scale structure, and constraints from COBE, Phys. Rev. D, 47, 426-455 (1993) |
| [52] | Vafa, C., Superstrings and topological strings at large \(N\), J. Math. Phys., 42, 2798-2817 (2001) · Zbl 1060.81594 |
| [53] | Cachazo, F.; Intriligator, K. A.; Vafa, C., A large N duality via a geometric transition, Nucl. Phys. B, 603, 3-41 (2001) · Zbl 0983.81050 |
| [54] | Dijkgraaf, R.; Vafa, C., A perturbative window into nonperturbative physics |
| [55] | Heckman, J. J.; Vafa, C., Geometrically induced phase transitions at large \(N\), J. High Energy Phys., 0804, Article 052 pp. (2008) · Zbl 1246.81257 |
| [56] | Aganagic, M.; Beem, C.; Kachru, S., Geometric transitions and dynamical SUSY breaking, Nucl. Phys. B, 796, 1-24 (2008) · Zbl 1219.81226 |
| [57] | Grimm, T. W., The \(N = 1\) effective action of F-theory compactifications, Nucl. Phys. B, 845, 48-92 (2011) · Zbl 1207.81120 |
| [58] | Alim, M.; Scheidegger, E., Topological strings on elliptic fibrations · Zbl 1316.81075 |
| [59] | Klemm, A.; Manschot, J.; Wotschke, T., Quantum geometry of elliptic Calabi-Yau manifolds · Zbl 1270.81180 |
| [60] | Grimm, T. W.; Weigand, T., On Abelian gauge symmetries and proton decay in global F-theory GUTs, Phys. Rev. D, 82, Article 086009 pp. (2010) |
| [61] | Morrison, D. R.; Park, D. S., F-theory and the Mordell-Weil group of elliptically-fibered Calabi-Yau threefolds, J. High Energy Phys., 1210, Article 128 pp. (2012) · Zbl 1397.81389 |
| [62] | Braun, V.; Grimm, T. W.; Keitel, J., New global F-theory GUTs with U(1) symmetries, J. High Energy Phys., 1309, Article 154 pp. (2013) |
| [63] | Cvetic, M.; Klevers, D.; Piragua, H., F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections, J. High Energy Phys., 1306, Article 067 pp. (2013) · Zbl 1342.81414 |
| [64] | Borchmann, J.; Mayrhofer, C.; Palti, E.; Weigand, T., Elliptic fibrations for \(SU(5) \times U(1) \times U(1) F\)-theory vacua, Phys. Rev. D, 88, 4, Article 046005 pp. (2013) |
| [65] | Grimm, T. W.; Kapfer, A.; Keitel, J., Effective action of 6D F-theory with U(1) factors: rational sections make Chern-Simons terms jump, J. High Energy Phys., 1307, Article 115 pp. (2013) · Zbl 1342.81286 |
| [66] | Braun, V.; Grimm, T. W.; Keitel, J., Geometric engineering in toric F-theory and GUTs with U(1) gauge factors, J. High Energy Phys., 1312, Article 069 pp. (2013) |
| [67] | Borchmann, J.; Mayrhofer, C.; Palti, E.; Weigand, T., SU(5) tops with multiple U(1) s in F-theory, Nucl. Phys. B, 882, 1-69 (2014) · Zbl 1285.81053 |
| [68] | Cvetic, M.; Klevers, D.; Piragua, H.; Song, P., Elliptic fibrations with rank three Mordell-Weil group: F-theory with U(1) x U(1) x U(1) gauge symmetry, J. High Energy Phys., 1403, Article 021 pp. (2014) |
| [69] | Braun, V.; Morrison, D. R., F-theory on genus-one fibrations · Zbl 1333.81200 |
| [70] | Morrison, D. R.; Taylor, W., Sections, multisections, and U(1) fields in F-theory · Zbl 1348.83091 |
| [71] | Kuntzler, M.; Schafer-Nameki, S., Tate trees for elliptic fibrations with rank one Mordell-Weil group |
| [72] | Klevers, D.; Pena, D. K.M.; Oehlmann, P.-K.; Piragua, H.; Reuter, J., F-theory on all toric hypersurface fibrations and its Higgs branches · Zbl 1388.81563 |
| [73] | Braun, V.; Grimm, T. W.; Keitel, J., Complete intersection fibers in F-theory · Zbl 1388.81294 |
| [74] | Lawrie, C.; Sacco, D., Tate’s algorithm for F-theory GUTs with two U(1)s |
| [75] | Anderson, L. B.; García-Etxebarria, I.; Grimm, T. W.; Keitel, J., Physics of F-theory compactifications without section · Zbl 1333.81299 |
| [76] | García-Etxebarria, I.; Grimm, T. W.; Keitel, J., Yukawas and discrete symmetries in F-theory compactifications without section, J. High Energy Phys., 1411, Article 125 pp. (2014) · Zbl 1333.81332 |
| [77] | Mayrhofer, C.; Palti, E.; Till, O.; Weigand, T., Discrete gauge symmetries by Higgsing in four-dimensional F-theory compactifications |
| [78] | Mayrhofer, C.; Palti, E.; Till, O.; Weigand, T., On discrete symmetries and torsion homology in F-theory · Zbl 1388.81353 |
| [79] | Mayr, P., Mirror symmetry, \(N = 1\) superpotentials and tensionless strings on Calabi-Yau four folds, Nucl. Phys. B, 494, 489-545 (1997) · Zbl 0938.81033 |
| [80] | Klemm, A.; Lian, B.; Roan, S.; Yau, S.-T., Calabi-Yau fourfolds for M theory and F theory compactifications, Nucl. Phys. B, 518, 515-574 (1998) · Zbl 0920.14016 |
| [81] | Alim, M.; Hecht, M.; Jockers, H.; Mayr, P.; Mertens, A., Hints for off-shell mirror symmetry in type II/F-theory compactifications, Nucl. Phys. B, 841, 303-338 (2010) · Zbl 1207.81093 |
| [82] | Grimm, T. W.; Ha, T.-W.; Klemm, A.; Klevers, D., Computing brane and flux superpotentials in F-theory compactifications, J. High Energy Phys., 1004, Article 015 pp. (2010) · Zbl 1272.81153 |
| [83] | Bizet, N. C.; Klemm, A.; Lopes, D. V., Landscaping with fluxes and the E8 Yukawa point in F-theory |
| [84] | Hebecker, A.; Kraus, S. C.; Lust, D.; Steinfurt, S.; Weigand, T., Fluxbrane inflation, Nucl. Phys. B, 854, 509-551 (2012) · Zbl 1229.83080 |
| [85] | Hebecker, A.; Kraus, S. C.; Kuntzler, M.; Lust, D.; Weigand, T., Fluxbranes: moduli stabilisation and inflation, J. High Energy Phys., 1301, Article 095 pp. (2013) · Zbl 1342.81434 |
| [86] | (Olver, F. W.J.; Lozier, D. W.; Boisvert, R. F.; Clark, C. W., NIST Handbook of Mathematical Functions (2010), Cambridge University Press: Cambridge University Press New York, NY), Print companion to [104] · Zbl 1198.00002 |
| [87] | Libgober, A., Chern classes and the periods of mirrors (1998) |
| [88] | Iritani, H., Real and integral structures in quantum cohomology I: toric orbifolds (2007) |
| [89] | Katzarkov, L.; Kontsevich, M.; Pantev, T., Hodge theoretic aspects of mirror symmetry (2008) · Zbl 1206.14009 |
| [90] | Iritani, H., An integral structure in quantum cohomology and mirror symmetry for toric orbifolds (2009) · Zbl 1190.14054 |
| [91] | Huang, M.-x.; Klemm, A.; Quackenbush, S., Topological string theory on compact Calabi-Yau: modularity and boundary conditions, Lect. Notes Phys., 757, 45-102 (2009) · Zbl 1166.81358 |
| [92] | Chen, Y.-H.; Yang, Y.; Yui, N., Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds (2006) |
| [93] | Candelas, P.; De La Ossa, X. C.; Green, P. S.; Parkes, L., A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B, 359, 21-74 (1991) · Zbl 1098.32506 |
| [94] | Danielsson, U. H.; Johansson, N.; Larfors, M., The world next door: results in landscape topography, J. High Energy Phys., 0703, Article 080 pp. (2007) |
| [95] | Johnson, M. C.; Larfors, M., Field dynamics and tunneling in a flux landscape, Phys. Rev. D, 78, Article 083534 pp. (2008) |
| [96] | Ahlqvist, P.; Greene, B. R.; Kagan, D.; Lim, E. A.; Sarangi, S., Conifolds and tunneling in the string landscape, J. High Energy Phys., 1103, Article 119 pp. (2011) · Zbl 1301.81173 |
| [97] | Braun, A. P.; Johansson, N.; Larfors, M.; Walliser, N.-O., Restrictions on infinite sequences of type IIB vacua, J. High Energy Phys., 1110, Article 091 pp. (2011) · Zbl 1303.81149 |
| [98] | Yang, I.-S., The strong multifield slowroll condition and spiral inflation, Phys. Rev. D, 85, Article 123532 pp. (2012) |
| [99] | Deligne, P., Courbes elliptiques: formulaire d’après J. Tate, Modular functions of one variable, (IV Proc. Internat. Summer Scholl (1972), Univ. Antwerp: Univ. Antwerp Antwerp) |
| [100] | Andreas, B.; Curio, G.; Klemm, A., Towards the standard model spectrum from elliptic Calabi-Yau, Int. J. Mod. Phys. A, 19, 1987 (2004) · Zbl 1080.81648 |
| [101] | Intriligator, K.; Jockers, H.; Mayr, P.; Morrison, D. R.; Plesser, M. R., Conifold transitions in M-theory on Calabi-Yau fourfolds with background fluxes, Adv. Theor. Math. Phys., 17, 601-699 (2013) · Zbl 1306.81251 |
| [102] | Grimm, T. W., Axion inflation in F-theory, Phys. Lett. B, 739, 201-208 (2014) · Zbl 1306.81411 |
| [103] | Jockers, H.; Louis, J., The effective action of D7-branes in \(N = 1\) Calabi-Yau orientifolds, Nucl. Phys. B, 705, 167-211 (2005) · Zbl 1119.81371 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
