Abstract
The fate of shift-symmetries in effective string models is considered beyond tree-level. Such symmetries have been proposed in the past as a way to maintain a hierarchically small Higgs mass and also play a role in schemes of cosmological relaxation. It is argued that on general grounds one expects shift-symmetries to be restored in the limit of certain asymmetric compactifications, to all orders in perturbation theory. This behaviour is verified by explicit computation of the Kähler potential to one-loop order.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. Lopes Cardoso, D. Lüst and T. Mohaupt, Moduli spaces and target space duality symmetries in (0, 2) Z N orbifold theories with continuous Wilson lines, Nucl. Phys. B 432 (1994) 68 [hep-th/9405002] [INSPIRE].
G. Lopes Cardoso, D. Lüst and T. Mohaupt, Threshold corrections and symmetry enhancement in string compactifications, Nucl. Phys. B 450 (1995) 115 [hep-th/9412209] [INSPIRE].
I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, Effective μ-term in superstring theory, Nucl. Phys. B 432 (1994) 187 [hep-th/9405024] [INSPIRE].
I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, Superstring threshold corrections to Yukawa couplings, Nucl. Phys. B 407 (1993) 706 [hep-th/9212045] [INSPIRE].
A. Brignole and F. Zwirner, Supersymmetry and SU(2) × U(1) breaking with naturally vanishing vacuum energy, Phys. Lett. B 342 (1995) 117 [hep-th/9409099] [INSPIRE].
A. Brignole, L.E. Ibáñez, C. Muñoz and C. Scheich, Some issues in soft SUSY breaking terms from dilaton/moduli sectors, Z. Phys. C 74 (1997) 157 [hep-ph/9508258] [INSPIRE].
G.R. Dvali and S. Pokorski, The role of the anomalous U(1)-A for the solution of the doublet-triplet splitting problem, Phys. Rev. Lett. 78 (1997) 807 [hep-ph/9610431] [INSPIRE].
Z.G. Berezhiani and G.R. Dvali, Possible solution of the hierarchy problem in supersymmetrical grand unification theories, Bull. Lebedev Phys. Inst. 5 (1989) 55 [Kratk. Soobshch. Fiz. 5 (1989) 42] [INSPIRE].
A. Hebecker, A.K. Knochel and T. Weigand, A Shift Symmetry in the Higgs Sector: Experimental Hints and Stringy Realizations, JHEP 06 (2012) 093 [arXiv:1204.2551] [INSPIRE].
A. Hebecker, A.K. Knochel and T. Weigand, The Higgs mass from a String-Theoretic Perspective, Nucl. Phys. B 874 (2013) 1 [arXiv:1304.2767] [INSPIRE].
H. Lüo and F. Zwirner, Geometrical hierarchies in classical supergravity, Phys. Rev. Lett. 113 (2014) 021801 [arXiv:1403.4942] [INSPIRE].
L.E. Ibáñez, F. Marchesano and I. Valenzuela, Higgs-otic Inflation and String Theory, JHEP 01 (2015) 128 [arXiv:1411.5380] [INSPIRE].
E. Kiritsis, String theory in a nutshell, Princeton University Press (2007).
S. Abel, K.R. Dienes and E. Mavroudi, Towards a nonsupersymmetric string phenomenology, Phys. Rev. D 91 (2015) 126014 [arXiv:1502.03087] [INSPIRE].
M. Berg, M. Haack and B. Körs, String loop corrections to Kähler potentials in orientifolds, JHEP 11 (2005) 030 [hep-th/0508043] [INSPIRE].
E. Kiritsis and N.A. Obers, Heterotic type-I duality in D < 10 dimensions, threshold corrections and D instantons, JHEP 10 (1997) 004 [hep-th/9709058] [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].
K. Forger and S. Stieberger, String amplitudes and N = 2, D = 4 prepotential in heterotic K3×T 2 compactifications, Nucl. Phys. B 514 (1998) 135 [hep-th/9709004] [INSPIRE].
B. de Wit, V. Kaplunovsky, J. Louis and D. Lüst, Perturbative couplings of vector multiplets in N = 2 heterotic string vacua, Nucl. Phys. B 451 (1995) 53 [hep-th/9504006] [INSPIRE].
E. Kiritsis, C. Kounnas, P.M. Petropoulos and J. Rizos, On the heterotic effective action at one loop gauge couplings and the gravitational sector, hep-th/9605011 [INSPIRE].
K. Foerger and S. Stieberger, Higher derivative couplings and heterotic type-I duality in eight-dimensions, Nucl. Phys. B 559 (1999) 277 [hep-th/9901020] [INSPIRE].
J.A. Harvey and G.W. Moore, Algebras, BPS states and strings, Nucl. Phys. B 463 (1996) 315 [hep-th/9510182] [INSPIRE].
I. Antoniadis, C. Bachas, C. Fabre, H. Partouche and T.R. Taylor, Aspects of type I-type II-heterotic triality in four-dimensions, Nucl. Phys. B 489 (1997) 160 [hep-th/9608012] [INSPIRE].
P.G. Camara and E. Dudas, Multi-instanton and string loop corrections in toroidal orbifold models, JHEP 08 (2008) 069 [arXiv:0806.3102] [INSPIRE].
N. Vanegas-Arbelaez, Regularization of automorphic functions of manifolds with special Kähler geometry, hep-th/9906028 [INSPIRE].
I. Antoniadis, E. Gava and K.S. Narain, Moduli corrections to gravitational couplings from string loops, Phys. Lett. B 283 (1992) 209 [hep-th/9203071] [INSPIRE].
C. Angelantonj, I. Florakis and M. Tsulaia, Universality of Gauge Thresholds in Non-Supersymmetric Heterotic Vacua, Phys. Lett. B 736 (2014) 365 [arXiv:1407.8023] [INSPIRE].
C. Bachas, C. Fabre, E. Kiritsis, N.A. Obers and P. Vanhove, Heterotic /type-I duality and D-brane instantons, Nucl. Phys. B 509 (1998) 33 [hep-th/9707126] [INSPIRE].
V. Kaplunovsky and J. Louis, On Gauge couplings in string theory, Nucl. Phys. B 444 (1995) 191 [hep-th/9502077] [INSPIRE].
M. Arends et al., D7-Brane Moduli Space in Axion Monodromy and Fluxbrane Inflation, Fortsch. Phys. 62 (2014) 647 [arXiv:1405.0283] [INSPIRE].
G. Dvali and A. Vilenkin, Cosmic attractors and gauge hierarchy, Phys. Rev. D 70 (2004) 063501 [hep-th/0304043] [INSPIRE].
G. Dvali, Large hierarchies from attractor vacua, Phys. Rev. D 74 (2006) 025018 [hep-th/0410286] [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].
A. Kobakhidze, Quantum relaxation of the Higgs mass, Eur. Phys. J. C 75 (2015) 384 [arXiv:1506.04840] [INSPIRE].
J.R. Espinosa, C. Grojean, G. Panico, A. Pomarol, O. Pujolàs and G. Servant, Cosmological Higgs-Axion Interplay for a Naturally Small Electroweak Scale, Phys. Rev. Lett. 115 (2015) 251803 [arXiv:1506.09217] [INSPIRE].
E. Hardy, Electroweak relaxation from finite temperature, JHEP 11 (2015) 077 [arXiv:1507.07525] [INSPIRE].
S.P. Patil and P. Schwaller, Relaxing the Electroweak Scale: the Role of Broken dS Symmetry, JHEP 02 (2016) 077 [arXiv:1507.08649] [INSPIRE].
O. Antipin and M. Redi, The Half-composite Two Higgs Doublet Model and the Relaxion, JHEP 12 (2015) 031 [arXiv:1508.01112] [INSPIRE].
J. Jaeckel, V.M. Mehta and L.T. Witkowski, Musings on cosmological relaxation and the hierarchy problem, arXiv:1508.03321 [INSPIRE].
R.S. Gupta, Z. Komargodski, G. Perez and L. Ubaldi, Is the Relaxion an Axion?, arXiv:1509.00047 [INSPIRE].
B. Batell, G.F. Giudice and M. McCullough, Natural Heavy Supersymmetry, JHEP 12 (2015) 162 [arXiv:1509.00834] [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, A Clockwork Axion, arXiv:1511.01827 [INSPIRE].
R. Kappl, H.P. Nilles and M.W. Winkler, Modulated Natural Inflation, Phys. Lett. B 753 (2016) 653 [arXiv:1511.05560] [INSPIRE].
L.E. Ibáñez, M. Montero, A. Uranga and I. Valenzuela, Relaxion Monodromy and the Weak Gravity Conjecture, arXiv:1512.00025 [INSPIRE].
K. Choi and H. Kim, Aligned natural inflation with modulations, arXiv:1511.07201 [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: 1511.02880
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
Abel, S., Stewart, R.J. Shift-symmetries at higher order. J. High Energ. Phys. 2016, 182 (2016). https://doi.org/10.1007/JHEP02(2016)182
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)182