Abstract
It has been recently argued that Higgsing of theories with U(1)n gauge interactions consistent with the Weak Gravity Conjecture (WGC) may lead to effective field theories parametrically violating WGC constraints. The minimal examples typically involve Higgs scalars with a large charge with respect to a U(1) (e.g. charges (Z, 1) in U(1)2 with Z ≫ 1). This type of Higgs multiplets play also a key role in clockwork U(1) theories. We study these issues in the context of heterotic string theory and find that, even if there is no new physics at the standard magnetic WGC scale Λ ∼ gIRM P , the string scale is just slightly above, at a scale \( \sim \sqrt{k_{\mathrm{IR}}}\varLambda \). Here kIR is the level of the IR U(1) worldsheet current. We show that, unlike the standard magnetic cutoff, this bound is insensitive to subsequent Higgsing. One may argue that this constraint gives rise to no bound at the effective field theory level since kIR is model dependent and in general unknown. However there is an additional constraint to be taken into account, which is that the Higgsing scalars with large charge Z should be part of the string massless spectrum, which becomes an upper bound kIR ≤ k 20 , where k0 is the level of the UV currents. Thus, for fixed k0, Z cannot be made parametrically large. The upper bound on the charges Z leads to limitations on the size and structure of hierarchies in an iterated U(1) clockwork mechanism.
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References
C. Vafa, The string landscape and the swampland, hep-th/0509212 [INSPIRE].
N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, The string landscape, black holes and gravity as the weakest force, JHEP 06 (2007) 060 [hep-th/0601001] [INSPIRE].
H. Ooguri and C. Vafa, On the Geometry of the String Landscape and the Swampland, Nucl. Phys. B 766 (2007) 21 [hep-th/0605264] [INSPIRE].
T. Rudelius, Constraints on axion inflation from the weak gravity conjecture, JCAP 09 (2015) 020 [arXiv:1503.00795] [INSPIRE].
M. Montero, A.M. Uranga and I. Valenzuela, Transplanckian axions!?, JHEP 08 (2015) 032 [arXiv:1503.03886] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, Fencing in the Swampland: quantum gravity constraints on large field inflation, JHEP 10 (2015) 023 [arXiv:1503.04783] [INSPIRE].
J. Brown, W. Cottrell, G. Shiu and P. Soler, On axionic field ranges, loopholes and the weak gravity conjecture, JHEP 04 (2016) 017 [arXiv:1504.00659] [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Weak gravity strongly constrains large-field axion inflation, JHEP 12 (2015) 108 [arXiv:1506.03447] [INSPIRE].
C. Cheung and G.N. Remmen, Naturalness and the Weak Gravity Conjecture, Phys. Rev. Lett. 113 (2014) 051601 [arXiv:1402.2287] [INSPIRE].
A. de la Fuente, P. Saraswat and R. Sundrum, Natural Inflation and Quantum Gravity, Phys. Rev. Lett. 114 (2015) 151303 [arXiv:1412.3457] [INSPIRE].
A. Hebecker, P. Mangat, F. Rompineve and L.T. Witkowski, Winding out of the Swamp: Evading the Weak Gravity Conjecture with F-term Winding Inflation?, Phys. Lett. B 748 (2015) 455 [arXiv:1503.07912] [INSPIRE].
T.C. Bachlechner, C. Long and L. McAllister, Planckian axions and the weak gravity conjecture, JHEP 01 (2016) 091 [arXiv:1503.07853] [INSPIRE].
T. Rudelius, On the possibility of large axion moduli spaces, JCAP 04 (2015) 049 [arXiv:1409.5793] [INSPIRE].
D. Junghans, Large-field inflation with multiple axions and the weak gravity conjecture, JHEP 02 (2016) 128 [arXiv:1504.03566] [INSPIRE].
K. Kooner, S. Parameswaran and I. Zavala, Warping the Weak Gravity Conjecture, Phys. Lett. B 759 (2016) 402 [arXiv:1509.07049] [INSPIRE].
D. Harlow, Wormholes, emergent gauge fields and the weak gravity conjecture, JHEP 01 (2016) 122 [arXiv:1510.07911] [INSPIRE].
L.E. Ibáñez, M. Montero, A. Uranga and I. Valenzuela, Relaxion monodromy and the weak gravity conjecture, JHEP 04 (2016) 020 [arXiv:1512.00025] [INSPIRE].
A. Hebecker, F. Rompineve and A. Westphal, Axion monodromy and the weak gravity conjecture, JHEP 04 (2016) 157 [arXiv:1512.03768] [INSPIRE].
M. Montero, G. Shiu and P. Soler, The weak gravity conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, arXiv:1610.01533 [INSPIRE].
B. Freivogel and M. Kleban, Vacua Morghulis, arXiv:1610.04564 [INSPIRE].
D. Klaewer and E. Palti, Super-Planckian spatial field variations and quantum gravity, JHEP 01 (2017) 088 [arXiv:1610.00010] [INSPIRE].
L. McAllister, P. Schwaller, G. Servant, J. Stout and A. Westphal, Runaway Relaxion Monodromy, arXiv:1610.05320 [INSPIRE].
A. Herraez and L.E. Ibáñez, An axion-induced SM/MSSM Higgs landscape and the weak gravity conjecture, JHEP 02 (2017) 109 [arXiv:1610.08836] [INSPIRE].
L.E. Ibáñez, V. Martin-Lozano and I. Valenzuela, Constraining neutrino masses, the cosmological constant and BSM physics from the weak gravity conjecture, JHEP 11 (2017) 066 [arXiv:1706.05392] [INSPIRE].
M. Montero, Are tiny gauge couplings out of the Swampland?, JHEP 10 (2017) 208 [arXiv:1708.02249] [INSPIRE].
P. Saraswat, Weak gravity conjecture and effective field theory, Phys. Rev. D 95 (2017) 025013 [arXiv:1608.06951] [INSPIRE].
L.E. Ibáñez and A.M. Uranga, String theory and particle physics: An introduction to string phenomenology, Cambridge University Press, Cambridge U.K. (2012).
P.H. Ginsparg, Gauge and Gravitational Couplings in Four-Dimensional String Theories, Phys. Lett. B 197 (1987) 139 [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Evidence for a sublattice weak gravity conjecture, JHEP 08 (2017) 025 [arXiv:1606.08437] [INSPIRE].
D.C. Lewellen, Embedding Higher Level Kac-Moody Algebras in Heterotic String Models, Nucl. Phys. B 337 (1990) 61 [INSPIRE].
A. Font, L.E. Ibáñez and F. Quevedo, Higher Level Kac-Moody String Models and Their Phenomenological Implications, Nucl. Phys. B 345 (1990) 389 [INSPIRE].
A.N. Schellekens, Electric Charge Quantization in String Theory, Phys. Lett. B 237 (1990) 363 [INSPIRE].
K. Choi and S.H. Im, Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry, JHEP 01 (2016) 149 [arXiv:1511.00132] [INSPIRE].
D.E. Kaplan and R. Rattazzi, Large field excursions and approximate discrete symmetries from a clockwork axion, Phys. Rev. D 93 (2016) 085007 [arXiv:1511.01827] [INSPIRE].
A. Ahmed and B.M. Dillon, Clockwork Goldstone Bosons, Phys. Rev. D 96 (2017) 115031 [arXiv:1612.04011] [INSPIRE].
G.F. Giudice and M. McCullough, A clockwork theory, JHEP 02 (2017) 036 [arXiv:1610.07962] [INSPIRE].
N. Craig, I. Garcia Garcia and D. Sutherland, Disassembling the clockwork mechanism, JHEP 10 (2017) 018 [arXiv:1704.07831] [INSPIRE].
H.M. Lee, Gauged U(1) clockwork theory, Phys. Lett. B 778 (2018) 79 [arXiv:1708.03564] [INSPIRE].
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Ibáñez, L.E., Montero, M. A note on the WGC, effective field theory and clockwork within string theory. J. High Energ. Phys. 2018, 57 (2018). https://doi.org/10.1007/JHEP02(2018)057
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DOI: https://doi.org/10.1007/JHEP02(2018)057