Abstract
The clockwork is a mechanism for generating light particles with exponentially suppressed interactions in theories which contain no small parameters at the fundamental level. We develop a general description of the clockwork mechanism valid for scalars, fermions, gauge bosons, and gravitons. This mechanism can be implemented with a discrete set of new fields or, in its continuum version, through an extra spatial dimension. In both cases the clockwork emerges as a useful tool for model-building applications. Notably, the continuum clockwork offers a solution to the Higgs naturalness problem, which turns out to be the same as in linear dilaton duals of Little String Theory. We also elucidate the similarities and differences of the continuum clockwork with large extra dimensions and warped spaces. All clockwork models, in the discrete and continuum, exhibit novel phenomenology with a distinctive spectrum of closely spaced resonances.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P.A.M. Dirac, The cosmological constants, Nature 139 (1937) 323 [INSPIRE].
P.A.M. Dirac, New basis for cosmology, Proc. Roy. Soc. Lond. A 165 (1938) 199.
G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking, NATO Sci. Ser. B 59 (1980) 135.
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].
P.W. Graham, D.E. Kaplan and S. Rajendran, Cosmological relaxation of the electroweak scale, Phys. Rev. Lett. 115 (2015) 221801 [arXiv:1504.07551] [INSPIRE].
N. Fonseca, L. de Lima, C.S. Machado and R.D. Matheus, Large field excursions from a few site relaxion model, Phys. Rev. D 94 (2016) 015010 [arXiv:1601.07183] [INSPIRE].
J.E. Kim, H.P. Nilles and M. Peloso, Completing natural inflation, JCAP 01 (2005) 005 [hep-ph/0409138] [INSPIRE].
K. Choi, H. Kim and S. Yun, Natural inflation with multiple sub-Planckian axions, Phys. Rev. D 90 (2014) 023545 [arXiv:1404.6209] [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].
T. Higaki and F. Takahashi, Natural and multi-natural inflation in axion landscape, JHEP 07 (2014) 074 [arXiv:1404.6923] [INSPIRE].
N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757 [hep-th/0104005] [INSPIRE].
C.T. Hill, S. Pokorski and J. Wang, Gauge invariant effective Lagrangian for Kaluza-Klein modes, Phys. Rev. D 64 (2001) 105005 [hep-th/0104035] [INSPIRE].
N. Arkani-Hamed, A.G. Cohen and H. Georgi, Electroweak symmetry breaking from dimensional deconstruction, Phys. Lett. B 513 (2001) 232 [hep-ph/0105239] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, The hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [INSPIRE].
L. Randall and R. Sundrum, A large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
I. Antoniadis, A. Arvanitaki, S. Dimopoulos and A. Giveon, Phenomenology of TeV little string theory from holography, Phys. Rev. Lett. 108 (2012) 081602 [arXiv:1102.4043] [INSPIRE].
O. Aharony, M. Berkooz, D. Kutasov and N. Seiberg, Linear dilatons, NS five-branes and holography, JHEP 10 (1998) 004 [hep-th/9808149] [INSPIRE].
O. Aharony, A. Giveon and D. Kutasov, LSZ in LST, Nucl. Phys. B 691 (2004) 3 [hep-th/0404016] [INSPIRE].
R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, BPS quantization of the five-brane, Nucl. Phys. B 486 (1997) 89 [hep-th/9604055] [INSPIRE].
R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, BPS spectrum of the five-brane and black hole entropy, Nucl. Phys. B 486 (1997) 77 [hep-th/9603126] [INSPIRE].
M. Berkooz, M. Rozali and N. Seiberg, Matrix description of M-theory on T 4 and T 5, Phys. Lett. B 408 (1997) 105 [hep-th/9704089] [INSPIRE].
N. Seiberg, New theories in six-dimensions and matrix description of M-theory on T 5 and \( {T}^5/{\mathbb{Z}}_2 \), Phys. Lett. B 408 (1997) 98 [hep-th/9705221] [INSPIRE].
R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, 5D black holes and matrix strings, Nucl. Phys. B 506 (1997) 121 [hep-th/9704018] [INSPIRE].
A. Losev, G.W. Moore and S.L. Shatashvili, M&m’s, Nucl. Phys. B 522 (1998) 105 [hep-th/9707250] [INSPIRE].
J.D. Lykken, Weak scale superstrings, Phys. Rev. D 54 (1996) R3693 [hep-th/9603133] [INSPIRE].
I. Antoniadis and B. Pioline, Low scale closed strings and their duals, Nucl. Phys. B 550 (1999) 41 [hep-th/9902055] [INSPIRE].
I. Antoniadis, S. Dimopoulos and A. Giveon, Little string theory at a TeV, JHEP 05 (2001) 055 [hep-th/0103033] [INSPIRE].
M. Baryakhtar, Graviton phenomenology of linear dilaton geometries, Phys. Rev. D 85 (2012) 125019 [arXiv:1202.6674] [INSPIRE].
P. Cox and T. Gherghetta, Radion dynamics and phenomenology in the linear dilaton model, JHEP 05 (2012) 149 [arXiv:1203.5870] [INSPIRE].
S.J. Brodsky and P. Hoyer, The \( \overline{h} \) expansion in quantum field theory, Phys. Rev. D 83 (2011) 045026 [arXiv:1009.2313] [INSPIRE].
A. Manohar and H. Georgi, Chiral quarks and the nonrelativistic quark model, Nucl. Phys. B 234 (1984) 189 [INSPIRE].
H. Georgi, Vector realization of chiral symmetry, Nucl. Phys. B 331 (1990) 311 [INSPIRE].
G.F. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The strongly-interacting light Higgs, JHEP 06 (2007) 045 [hep-ph/0703164] [INSPIRE].
A. Pomarol, Higgs physics, in the proceedings of the 2014 European School of High-Energy Physics (ESHEP 2014), June 18-July 1, Garderen, The Netherlands, (2014), arXiv:1412.4410 [INSPIRE].
G. Panico and A. Wulzer, The composite Nambu-Goldstone Higgs, Lect. Notes Phys. 913 (2016) 1 [arXiv:1506.01961].
T. Higaki, K.S. Jeong, N. Kitajima and F. Takahashi, The QCD axion from aligned axions and diphoton excess, Phys. Lett. B 755 (2016) 13 [arXiv:1512.05295] [INSPIRE].
T. Higaki, K.S. Jeong, N. Kitajima and F. Takahashi, Quality of the Peccei-Quinn symmetry in the Aligned QCD Axion and Cosmological Implications, JHEP 06 (2016) 150 [arXiv:1603.02090] [INSPIRE].
T. Higaki, K.S. Jeong, N. Kitajima, T. Sekiguchi and F. Takahashi, Topological defects and nano-Hz gravitational waves in aligned axion models, JHEP 08 (2016) 044 [arXiv:1606.05552] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos, G.R. Dvali and J. March-Russell, Neutrino masses from large extra dimensions, Phys. Rev. D 65 (2001) 024032 [hep-ph/9811448] [INSPIRE].
N. Arkani-Hamed, H. Georgi and M.D. Schwartz, Effective field theory for massive gravitons and gravity in theory space, Annals Phys. 305 (2003) 96 [hep-th/0210184] [INSPIRE].
K.A. Meissner and M. Olechowski, General warped solutions in 5D dilaton gravity, Class. Quant. Grav. 20 (2003) 5391 [hep-th/0305170] [INSPIRE].
O. DeWolfe, D.Z. Freedman, S.S. Gubser and A. Karch, Modeling the fifth-dimension with scalars and gravity, Phys. Rev. D 62 (2000) 046008 [hep-th/9909134] [INSPIRE].
W.D. Goldberger and M.B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
N. Arkani-Hamed, A.G. Cohen, D.B. Kaplan, A. Karch and L. Motl, Deconstructing (2, 0) and little string theories, JHEP 01 (2003) 083 [hep-th/0110146] [INSPIRE].
G. Burdman, N. Fonseca and L. de Lima, Full-hierarchy quiver theories of electroweak symmetry breaking and fermion masses, JHEP 01 (2013) 094 [arXiv:1210.5568] [INSPIRE].
G. Burdman, P. Ormonde and V. Peralta, Fermion resonances in quiver theories with a PNGB Higgs, JHEP 11 (2014) 045 [arXiv:1408.1320] [INSPIRE].
G. Burdman, N. Fonseca and G. Lichtenstein, Resonances from quiver theories at the LHC, Phys. Rev. D 88 (2013) 116006 [arXiv:1308.5988] [INSPIRE].
G.F. Giudice, T. Plehn and A. Strumia, Graviton collider effects in one and more large extra dimensions, Nucl. Phys. B 706 (2005) 455 [hep-ph/0408320] [INSPIRE].
N. Kaloper, J. March-Russell, G.D. Starkman and M. Trodden, Compact hyperbolic extra dimensions: branes, Kaluza-Klein modes and cosmology, Phys. Rev. Lett. 85 (2000) 928 [hep-ph/0002001] [INSPIRE].
I.R. Klebanov and E. Witten, Superconformal field theory on three-branes at a Calabi-Yau singularity, Nucl. Phys. B 536 (1998) 199 [hep-th/9807080] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: duality cascades and χ SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [INSPIRE].
C. Csáki, C. Grojean, J. Hubisz, Y. Shirman and J. Terning, Fermions on an interval: quark and lepton masses without a Higgs, Phys. Rev. D 70 (2004) 015012 [hep-ph/0310355] [INSPIRE].
C. Csáki, J. Hubisz and S.J. Lee, Radion phenomenology in realistic warped space models, Phys. Rev. D 76 (2007) 125015 [arXiv:0705.3844] [INSPIRE].
Y. Bai, G. Burdman and C.T. Hill, Topological interactions in warped extra dimensions, JHEP 02 (2010) 049 [arXiv:0911.1358] [INSPIRE].
M.D. Schwartz, Constructing gravitational dimensions, Phys. Rev. D 68 (2003) 024029 [hep-th/0303114] [INSPIRE].
L. Randall, M.D. Schwartz and S. Thambyahpillai, Discretizing gravity in warped spacetime, JHEP 10 (2005) 110 [hep-th/0507102] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1610.07962
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Giudice, G.F., McCullough, M. A clockwork theory. J. High Energ. Phys. 2017, 36 (2017). https://doi.org/10.1007/JHEP02(2017)036
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2017)036