Abstract
We study primordial electromagnetic fields in effective actions of string theory. In contrast to a conventional scenario of producing primordial electromagnetic fields induced by the axion inflation, we deal with the Dirac-Born-Infeld action as a non-linear generation of Maxwell theory. It turns out that the intensity of generated electromagnetic fields is bounded from above by the string scale which can also be rewritten in terms of supersymmetry breaking scale in the context of type IIB Large Volume Scenario. The instability parameter ξ is constrained by the tadpole cancellation condition of D3-branes and a realization of hierarchy between the string scale and the Hubble scale of inflation. Hence, the magnetogenesis can be realized in the limited corner of the string landscape due to the \( \mathcal{O} \)(1) value of the coefficient of Chern-Simons coupling.
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K. Freese, J.A. Frieman and A.V. Olinto, Natural inflation with pseudo-Nambu-Goldstone bosons, Phys. Rev. Lett. 65 (1990) 3233 [INSPIRE].
F.C. Adams et al., Natural inflation: Particle physics models, power law spectra for large scale structure, and constraints from COBE, Phys. Rev. D 47 (1993) 426 [hep-ph/9207245] [INSPIRE].
L. McAllister, E. Silverstein and A. Westphal, Gravity Waves and Linear Inflation from Axion Monodromy, Phys. Rev. D 82 (2010) 046003 [arXiv:0808.0706] [INSPIRE].
Planck collaboration, Planck 2018 results. X. Constraints on inflation, Astron. Astrophys. 641 (2020) A10 [arXiv:1807.06211] [INSPIRE].
S.M. Carroll, G.B. Field and R. Jackiw, Limits on a Lorentz and Parity Violating Modification of Electrodynamics, Phys. Rev. D 41 (1990) 1231 [INSPIRE].
M.M. Anber and L. Sorbo, N-flationary magnetic fields, JCAP 10 (2006) 018 [astro-ph/0606534] [INSPIRE].
P.A. Davidson, An introduction to magnetohydrodynamics, Cambridge University Press, Cambridge, U.K. (2001).
Y. Akamatsu and N. Yamamoto, Chiral Plasma Instabilities, Phys. Rev. Lett. 111 (2013) 052002 [arXiv:1302.2125] [INSPIRE].
A. Ohnishi and N. Yamamoto, Magnetars and the Chiral Plasma Instabilities, arXiv:1402.4760 [INSPIRE].
N. Yamamoto and R. Yokokura, Generalized chiral instabilities, linking numbers, and non-invertible symmetries, JHEP 07 (2023) 045 [arXiv:2305.01234] [INSPIRE].
K. Kamada, N. Yamamoto and D.-L. Yang, Chiral effects in astrophysics and cosmology, Prog. Part. Nucl. Phys. 129 (2023) 104016 [arXiv:2207.09184] [INSPIRE].
M.S. Turner and L.M. Widrow, Inflation Produced, Large Scale Magnetic Fields, Phys. Rev. D 37 (1988) 2743 [INSPIRE].
W.D. Garretson, G.B. Field and S.M. Carroll, Primordial magnetic fields from pseudoGoldstone bosons, Phys. Rev. D 46 (1992) 5346 [hep-ph/9209238] [INSPIRE].
N. Barnaby, E. Pajer and M. Peloso, Gauge Field Production in Axion Inflation: Consequences for Monodromy, non-Gaussianity in the CMB, and Gravitational Waves at Interferometers, Phys. Rev. D 85 (2012) 023525 [arXiv:1110.3327] [INSPIRE].
T. Fujita et al., Consistent generation of magnetic fields in axion inflation models, JCAP 05 (2015) 054 [arXiv:1503.05802] [INSPIRE].
M.M. Anber and E. Sabancilar, Hypermagnetic Fields and Baryon Asymmetry from Pseudoscalar Inflation, Phys. Rev. D 92 (2015) 101501 [arXiv:1507.00744] [INSPIRE].
P. Adshead, J.T. Giblin, T.R. Scully and E.I. Sfakianakis, Magnetogenesis from axion inflation, JCAP 10 (2016) 039 [arXiv:1606.08474] [INSPIRE].
M. Ballardini et al., Energy-momentum tensor and helicity for gauge fields coupled to a pseudo-scalar inflaton, Phys. Rev. D 100 (2019) 123542 [Erratum ibid. 105 (2022) 069905] [arXiv:1910.13448] [INSPIRE].
M. Giovannini and M.E. Shaposhnikov, Primordial hypermagnetic fields and triangle anomaly, Phys. Rev. D 57 (1998) 2186 [hep-ph/9710234] [INSPIRE].
K. Bamba, Baryon asymmetry from hypermagnetic helicity in dilaton hypercharge electromagnetism, Phys. Rev. D 74 (2006) 123504 [hep-ph/0611152] [INSPIRE].
T. Fujita and K. Kamada, Large-scale magnetic fields can explain the baryon asymmetry of the Universe, Phys. Rev. D 93 (2016) 083520 [arXiv:1602.02109] [INSPIRE].
K. Kamada and A.J. Long, Baryogenesis from decaying magnetic helicity, Phys. Rev. D 94 (2016) 063501 [arXiv:1606.08891] [INSPIRE].
K. Kamada and A.J. Long, Evolution of the Baryon Asymmetry through the Electroweak Crossover in the Presence of a Helical Magnetic Field, Phys. Rev. D 94 (2016) 123509 [arXiv:1610.03074] [INSPIRE].
Y. Cado and E. Sabancilar, Asymmetric Dark Matter and Baryogenesis from Pseudoscalar Inflation, JCAP 04 (2017) 047 [arXiv:1611.02293] [INSPIRE].
D. Jiménez, K. Kamada, K. Schmitz and X.-J. Xu, Baryon asymmetry and gravitational waves from pseudoscalar inflation, JCAP 12 (2017) 011 [arXiv:1707.07943] [INSPIRE].
R. Durrer and A. Neronov, Cosmological Magnetic Fields: Their Generation, Evolution and Observation, Astron. Astrophys. Rev. 21 (2013) 62 [arXiv:1303.7121] [INSPIRE].
K. Subramanian, The origin, evolution and signatures of primordial magnetic fields, Rept. Prog. Phys. 79 (2016) 076901 [arXiv:1504.02311] [INSPIRE].
R. Blumenhagen, B. Kors, D. Lüst and S. Stieberger, Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes, Phys. Rept. 445 (2007) 1 [hep-th/0610327] [INSPIRE].
L.E. Ibanez and A.M. Uranga, String theory and particle physics: An introduction to string phenomenology, Cambridge University Press (2012) [INSPIRE].
V. Balasubramanian, P. Berglund, J.P. Conlon and F. Quevedo, Systematics of moduli stabilisation in Calabi-Yau flux compactifications, JHEP 03 (2005) 007 [hep-th/0502058] [INSPIRE].
J.P. Conlon, F. Quevedo and K. Suruliz, Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking, JHEP 08 (2005) 007 [hep-th/0505076] [INSPIRE].
K. Choi and J.E. Kim, Harmful Axions in Superstring Models, Phys. Lett. B 154 (1985) 393 [Erratum ibid. 156 (1985) 452] [INSPIRE].
T. Banks, M. Dine, P.J. Fox and E. Gorbatov, On the possibility of large axion decay constants, JCAP 06 (2003) 001 [hep-th/0303252] [INSPIRE].
P. Svrcek and E. Witten, Axions In String Theory, JHEP 06 (2006) 051 [hep-th/0605206] [INSPIRE].
V. Domcke and K. Mukaida, Gauge Field and Fermion Production during Axion Inflation, JCAP 11 (2018) 020 [arXiv:1806.08769] [INSPIRE].
O.O. Sobol, E.V. Gorbar and S.I. Vilchinskii, Backreaction of electromagnetic fields and the Schwinger effect in pseudoscalar inflation magnetogenesis, Phys. Rev. D 100 (2019) 063523 [arXiv:1907.10443] [INSPIRE].
T. Fujita, J. Kume, K. Mukaida and Y. Tada, Effective treatment of U(1) gauge field and charged particles in axion inflation, JCAP 09 (2022) 023 [arXiv:2204.01180] [INSPIRE].
R. von Eckardstein et al., Axion inflation in the strong-backreaction regime: decay of the Anber-Sorbo solution, JHEP 11 (2023) 183 [arXiv:2309.04254] [INSPIRE].
I. Bena, J. Blåbäck, M. Graña and S. Lüst, The tadpole problem, JHEP 11 (2021) 223 [arXiv:2010.10519] [INSPIRE].
K. Ishiguro et al., Upper bound on the Atiyah-Singer index from tadpole cancellation, JHEP 01 (2020) 200 [arXiv:2308.12421] [INSPIRE].
V. Domcke, Y. Ema and K. Mukaida, Chiral Anomaly, Schwinger Effect, Euler-Heisenberg Lagrangian, and application to axion inflation, JHEP 02 (2020) 055 [arXiv:1910.01205] [INSPIRE].
R. Blumenhagen, D. Lüst and S. Theisen, Basic concepts of string theory, Springer, Heidelberg, Germany (2013) [https://doi.org/10.1007/978-3-642-29497-6] [INSPIRE].
K. Becker and M. Becker, M theory on eight manifolds, Nucl. Phys. B 477 (1996) 155 [hep-th/9605053] [INSPIRE].
S. Sethi, C. Vafa and E. Witten, Constraints on low dimensional string compactifications, Nucl. Phys. B 480 (1996) 213 [hep-th/9606122] [INSPIRE].
S. Gukov, C. Vafa and E. Witten, CFT’s from Calabi-Yau four folds, Nucl. Phys. B 584 (2000) 69 [hep-th/9906070] [INSPIRE].
F. Denef et al., Fixing all moduli in a simple f-theory compactification, Adv. Theor. Math. Phys. 9 (2005) 861 [hep-th/0503124] [INSPIRE].
Y. Honma and H. Otsuka, On the Flux Vacua in F-theory Compactifications, Phys. Lett. B 774 (2017) 225 [arXiv:1706.09417] [INSPIRE].
C. Bachas and M. Porrati, Pair creation of open strings in an electric field, Phys. Lett. B 296 (1992) 77 [hep-th/9209032] [INSPIRE].
M. Cicoli, J.P. Conlon, A. Maharana and F. Quevedo, A Note on the Magnitude of the Flux Superpotential, JHEP 01 (2014) 027 [arXiv:1310.6694] [INSPIRE].
M. Demirtas, M. Kim, L. Mcallister and J. Moritz, Vacua with Small Flux Superpotential, Phys. Rev. Lett. 124 (2020) 211603 [arXiv:1912.10047] [INSPIRE].
M. Demirtas, M. Kim, L. McAllister and J. Moritz, Conifold Vacua with Small Flux Superpotential, Fortsch. Phys. 68 (2020) 2000085 [arXiv:2009.03312] [INSPIRE].
R. Álvarez-García, R. Blumenhagen, M. Brinkmann and L. Schlechter, Small Flux Superpotentials for Type IIB Flux Vacua Close to a Conifold, Fortsch. Phys. 68 (2020) 2000088 [arXiv:2009.03325] [INSPIRE].
Y. Honma and H. Otsuka, Small flux superpotential in F-theory compactifications, Phys. Rev. D 103 (2021) 126022 [arXiv:2103.03003] [INSPIRE].
T. Higaki and F. Takahashi, Dark Radiation and Dark Matter in Large Volume Compactifications, JHEP 11 (2012) 125 [arXiv:1208.3563] [INSPIRE].
L. Aparicio et al., Sequestered de Sitter String Scenarios: Soft-terms, JHEP 11 (2014) 071 [arXiv:1409.1931] [INSPIRE].
M. Cicoli et al., D-Branes at del Pezzo Singularities: Global Embedding and Moduli Stabilisation, JHEP 09 (2012) 019 [arXiv:1206.5237] [INSPIRE].
M. Cicoli et al., D3/D7 Branes at Singularities: Constraints from Global Embedding and Moduli Stabilisation, JHEP 07 (2013) 150 [arXiv:1304.0022] [INSPIRE].
M. Cicoli et al., Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter, JHEP 05 (2014) 001 [arXiv:1312.0014] [INSPIRE].
M. Cicoli et al., Global Orientifolded Quivers with Inflation, JHEP 11 (2017) 134 [arXiv:1706.06128] [INSPIRE].
M. Cicoli et al., The Standard Model quiver in de Sitter string compactifications, JHEP 08 (2021) 109 [arXiv:2106.11964] [INSPIRE].
M. Cicoli, A. Maharana, F. Quevedo and C.P. Burgess, De Sitter String Vacua from Dilaton-dependent Non-perturbative Effects, JHEP 06 (2012) 011 [arXiv:1203.1750] [INSPIRE].
M. Cicoli, A. Cotellucci and H. Otsuka, Sequestered string models imply split supersymmetry, JHEP 01 (2024) 059 [arXiv:2309.05752] [INSPIRE].
J.D. Finke et al., Constraints on the Intergalactic Magnetic Field with Gamma-Ray Observations of Blazars, Astrophys. J. 814 (2015) 20 [arXiv:1510.02485] [INSPIRE].
Fermi-LAT collaboration, The Search for Spatial Extension in High-latitude Sources Detected by the Fermi Large Area Telescope, Astrophys. J. Suppl. 237 (2018) 32 [arXiv:1804.08035] [INSPIRE].
V. Domcke, V. Guidetti, Y. Welling and A. Westphal, Resonant backreaction in axion inflation, JCAP 09 (2020) 009 [arXiv:2002.02952] [INSPIRE].
H. Abe, T. Kobayashi and H. Otsuka, Towards natural inflation from weakly coupled heterotic string theory, PTEP 2015 (2015) 063E02 [arXiv:1409.8436] [INSPIRE].
T. Ali, S.S. Haque and V. Jejjala, Natural Inflation from Near Alignment in Heterotic String Theory, Phys. Rev. D 91 (2015) 083516 [arXiv:1410.4660] [INSPIRE].
L.J. Dixon, V. Kaplunovsky and J. Louis, Moduli dependence of string loop corrections to gauge coupling constants, Nucl. Phys. B 355 (1991) 649 [INSPIRE].
D. Lüst and S. Stieberger, Gauge threshold corrections in intersecting brane world models, Fortsch. Phys. 55 (2007) 427 [hep-th/0302221] [INSPIRE].
J.P. Conlon and S. Krippendorf, Axion decay constants away from the lamppost, JHEP 04 (2016) 085 [arXiv:1601.00647] [INSPIRE].
M. Honda, A. Oikawa and H. Otsuka, Axion decay constants at special points in type II string theory, JHEP 01 (2017) 064 [arXiv:1608.08372] [INSPIRE].
F. Marchesano and G. Shiu, Building MSSM flux vacua, JHEP 11 (2004) 041 [hep-th/0409132] [INSPIRE].
M. Haack and J. Louis, M theory compactified on Calabi-Yau fourfolds with background flux, Phys. Lett. B 507 (2001) 296 [hep-th/0103068] [INSPIRE].
R. Blumenhagen, V. Braun, T.W. Grimm and T. Weigand, GUTs in Type IIB Orientifold Compactifications, Nucl. Phys. B 815 (2009) 1 [arXiv:0811.2936] [INSPIRE].
P. Candelas, E. Perevalov and G. Rajesh, Toric geometry and enhanced gauge symmetry of F theory / heterotic vacua, Nucl. Phys. B 507 (1997) 445 [hep-th/9704097] [INSPIRE].
W. Taylor and Y.-N. Wang, The F-theory geometry with most flux vacua, JHEP 12 (2015) 164 [arXiv:1511.03209] [INSPIRE].
Acknowledgments
We thank K. Kamada and K. Mukaida for helpful discussions and comments. This work was supported by JSPS KAKENHI Grant Numbers JP20K14477 (H. O.), JP21J00480 (R. Y.), JP21K13928 (R. Y.), JP23H04512 (H. O).
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Otsuka, H., Yokokura, R. Stringy constraints on primordial electromagnetic fields in axion inflation. J. High Energ. Phys. 2024, 55 (2024). https://doi.org/10.1007/JHEP07(2024)055
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DOI: https://doi.org/10.1007/JHEP07(2024)055