Abstract
It has been recently argued that an embedding of the SM into a consistent theory of quantum gravity may imply important constraints on the mass of the lightest neutrino and the cosmological constant Λ4. The constraints come from imposing the absence of any non-SUSY AdS stable vacua obtained from any consistent compactification of the SM to 3 or 2 dimensions. This condition comes as a corollary of a recent extension of the Weak Gravity Conjecture (WGC) by Ooguri and Vafa. In this paper we study T 2/Z N compactifications of the SM to two dimensions in which SM Wilson lines are projected out, leading to a considerable simplification. We analyze in detail a T 2/Z4 compactification of the SM in which both complex structure and Wilson line scalars are fixed and the potential is only a function of the area of the torus a2. We find that the SM is not robust against the appearance of AdS vacua in 2D and hence would be by itself inconsistent with quantum gravity. On the contrary, if the SM is embedded at some scale M SS into a SUSY version like the MSSM, the AdS vacua present in the non-SUSY case disappear or become unstable. This means that WGC arguments favor a SUSY version of the SM, independently of the usual hierarchy problem arguments. In a T 2/Z4 compactification in which the orbifold action is embedded into the B − L symmetry the bounds on neutrino masses and the cosmological constant are recovered. This suggests that the MSSM should be extended with a U(1)B−L gauge group. In other families of vacua the spectrum of SUSY particles is further constrained in order to avoid the appearance of new AdS vacua or instabilities. We discuss a possible understanding of the little hierarchy problem in this context.
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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].
B. Heidenreich, M. Reece and T. Rudelius, Evidence for a sublattice weak gravity conjecture, JHEP 08 (2017) 025 [arXiv:1606.08437] [INSPIRE].
M. Montero, G. Shiu and P. Soler, The Weak Gravity Conjecture in three dimensions, JHEP 10 (2016) 159 [arXiv:1606.08438] [INSPIRE].
P. Saraswat, Weak gravity conjecture and effective field theory, Phys. Rev. D 95 (2017) 025013 [arXiv:1608.06951] [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, JHEP 02 (2018) 124 [arXiv:1610.05320] [INSPIRE].
A. Herráez and L.E. Ibáñez, An Axion-induced SM/MSSM Higgs Landscape and the Weak Gravity Conjecture, JHEP 02 (2017) 109 [arXiv:1610.08836] [INSPIRE].
M. Montero, Are tiny gauge couplings out of the Swampland?, JHEP 10 (2017) 208 [arXiv:1708.02249] [INSPIRE].
L.E. Ibáñez and M. Montero, A Note on the WGC, Effective Field Theory and Clockwork within String Theory, JHEP 02 (2018) 057 [arXiv:1709.02392] [INSPIRE].
C. Cheung, J. Liu and G.N. Remmen, Proof of the Weak Gravity Conjecture from Black Hole Entropy, arXiv:1801.08546 [INSPIRE].
T.W. Grimm, E. Palti and I. Valenzuela, Infinite Distances in Field Space and Massless Towers of States, arXiv:1802.08264 [INSPIRE].
B. Heidenreich, M. Reece and T. Rudelius, Emergence and the Swampland Conjectures, arXiv:1802.08698 [INSPIRE].
S. Andriolo, D. Junghans, T. Noumi and G. Shiu, A Tower Weak Gravity Conjecture from Infrared Consistency, arXiv:1802.04287 [INSPIRE].
R. Blumenhagen, D. Kläwer, L. Schlechter and F. Wolf, The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces, arXiv:1803.04989 [INSPIRE].
T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland and the Missing Corner, arXiv:1711.00864 [INSPIRE].
H. Ooguri and C. Vafa, Non-supersymmetric AdS and the Swampland, Adv. Theor. Math. Phys. 21 (2017) 1787 [arXiv:1610.01533] [INSPIRE].
U. Danielsson and G. Dibitetto, Fate of stringy AdS vacua and the weak gravity conjecture, Phys. Rev. D 96 (2017) 026020 [arXiv:1611.01395] [INSPIRE].
B. Freivogel and M. Kleban, Vacua Morghulis, arXiv:1610.04564 [INSPIRE].
T. Banks, Note on a Paper by Ooguri and Vafa, arXiv:1611.08953 [INSPIRE].
H. Ooguri and L. Spodyneiko, New Kaluza-Klein instantons and the decay of AdS vacua, Phys. Rev. D 96 (2017) 026016 [arXiv:1703.03105] [INSPIRE].
S. Giombi, Higher Spin — CFT Duality, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (TASI 2015): Boulder, CO, U.S.A., June 1-26, 2015, pp. 137-214, arXiv:1607.02967 [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].
L.E. Ibáñez, V. Martin-Lozano and I. Valenzuela, Constraining the EW Hierarchy from the Weak Gravity Conjecture, arXiv:1707.05811 [INSPIRE].
N. Arkani-Hamed, S. Dubovsky, A. Nicolis and G. Villadoro, Quantum Horizons of the Standard Model Landscape, JHEP 06 (2007) 078 [hep-th/0703067] [INSPIRE].
Y. Hamada and G. Shiu, Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape, JHEP 11 (2017) 043 [arXiv:1707.06326] [INSPIRE].
Particle Data Group collaboration, C. Patrignani et al., Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, Dimensionless constants, cosmology and other dark matters, Phys. Rev. D 73 (2006) 023505 [astro-ph/0511774] [INSPIRE].
L. Pogosian and A. Vilenkin, Anthropic predictions for vacuum energy and neutrino masses in the light of WMAP-3, JCAP 01 (2007) 025 [astro-ph/0611573] [INSPIRE].
L.E. Ibáñez and A.M. Uranga, Neutrino Majorana Masses from String Theory Instanton Effects, JHEP 03 (2007) 052 [hep-th/0609213] [INSPIRE].
R. Blumenhagen, M. Cvetič and T. Weigand, Spacetime instanton corrections in 4D string vacua: The seesaw mechanism for D-brane models, Nucl. Phys. B 771 (2007) 113 [hep-th/0609191] [INSPIRE].
L.E. Ibáñez, A.N. Schellekens and A.M. Uranga, Instanton Induced Neutrino Majorana Masses in CFT Orientifolds with MSSM-like spectra, JHEP 06 (2007) 011 [arXiv:0704.1079] [INSPIRE].
T. Appelquist and A. Chodos, The Quantum Dynamics of Kaluza-Klein Theories, Phys. Rev. D 28 (1983) 772 [INSPIRE].
E. Ponton and E. Poppitz, Casimir energy and radius stabilization in five-dimensional orbifolds and six-dimensional orbifolds, JHEP 06 (2001) 019 [hep-ph/0105021] [INSPIRE].
E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].
N. Cabibbo, L. Maiani, G. Parisi and R. Petronzio, Bounds on the Fermions and Higgs Boson Masses in Grand Unified Theories, Nucl. Phys. B 158 (1979) 295 [INSPIRE].
J.A. Casas, J.R. Espinosa and M. Quirós, Improved Higgs mass stability bound in the standard model and implications for supersymmetry, Phys. Lett. B 342 (1995) 171 [hep-ph/9409458] [INSPIRE].
G. Altarelli and G. Isidori, Lower limit on the Higgs mass in the standard model: An update, Phys. Lett. B 337 (1994) 141 [INSPIRE].
J.A. Casas, J.R. Espinosa and M. Quirós, Standard model stability bounds for new physics within LHC reach, Phys. Lett. B 382 (1996) 374 [hep-ph/9603227] [INSPIRE].
J. Elias-Miro, J.R. Espinosa, G.F. Giudice, G. Isidori, A. Riotto and A. Strumia, Higgs mass implications on the stability of the electroweak vacuum, Phys. Lett. B 709 (2012) 222 [arXiv:1112.3022] [INSPIRE].
G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].
L.E. Ibáñez and I. Valenzuela, The Higgs Mass as a Signature of Heavy SUSY, JHEP 05 (2013) 064 [arXiv:1301.5167] [INSPIRE].
L.E. Ibáñez, F. Marchesano, D. Regalado and I. Valenzuela, The Intermediate Scale MSSM, the Higgs Mass and F-theory Unification, JHEP 07 (2012) 195 [arXiv:1206.2655] [INSPIRE].
J.M. Arnold, B. Fornal and M.B. Wise, Standard Model Vacua for Two-dimensional Compactifications, JHEP 12 (2010) 083 [arXiv:1010.4302] [INSPIRE].
J.M. Arnold, B. Fornal and K. Ishiwata, Finite Temperature Structure of the Compactified Standard Model, JHEP 08 (2011) 030 [arXiv:1103.0002] [INSPIRE].
D.M. Ghilencea, D. Hoover, C.P. Burgess and F. Quevedo, Casimir energies for 6D supergravities compactified on T 2 /Z N with Wilson lines, JHEP 09 (2005) 050 [hep-th/0506164] [INSPIRE].
L.E. Ibáñez, A.N. Schellekens and A.M. Uranga, Discrete Gauge Symmetries in Discrete MSSM-like Orientifolds, Nucl. Phys. B 865 (2012) 509 [arXiv:1205.5364] [INSPIRE].
M. Berasaluce-Gonzalez, L.E. Ibáñez, P. Soler and A.M. Uranga, Discrete gauge symmetries in D-brane models, JHEP 12 (2011) 113 [arXiv:1106.4169] [INSPIRE].
A. Font, L.E. Ibáñez, F. Quevedo and A. Sierra, The Construction of ‘Realistic’ Four-Dimensional Strings Through Orbifolds, Nucl. Phys. B 331 (1990) 421 [INSPIRE].
H.P. Nilles, Stringy Origin of Discrete R-symmetries, PoS(CORFU2016)017 [arXiv:1705.01798] [INSPIRE].
T. Kobayashi, H.P. Nilles, F. Ploger, S. Raby and M. Ratz, Stringy origin of non-Abelian discrete flavor symmetries, Nucl. Phys. B 768 (2007) 135 [hep-ph/0611020] [INSPIRE].
H.M. Lee et al., Discrete R symmetries for the MSSM and its singlet extensions, Nucl. Phys. B 850 (2011) 1 [arXiv:1102.3595] [INSPIRE].
M. Berasaluce-Gonzalez, P.G. Camara, F. Marchesano, D. Regalado and A.M. Uranga, Non-Abelian discrete gauge symmetries in 4d string models, JHEP 09 (2012) 059 [arXiv:1206.2383] [INSPIRE].
P. Anastasopoulos, R. Richter and A.N. Schellekens, Discrete symmetries from hidden sectors, JHEP 06 (2015) 189 [arXiv:1502.02686] [INSPIRE].
T.P.T. Dijkstra, L.R. Huiszoon and A.N. Schellekens, Supersymmetric standard model spectra from RCFT orientifolds, Nucl. Phys. B 710 (2005) 3 [hep-th/0411129] [INSPIRE].
B. Gato-Rivera and A.N. Schellekens, Asymmetric Gepner Models III. B-L Lifting, Nucl. Phys. B 847 (2011) 532 [arXiv:1012.0796] [INSPIRE].
G. Honecker and W. Staessens, To Tilt or Not To Tilt: Discrete Gauge Symmetries in Global Intersecting D-brane Models, JHEP 10 (2013) 146 [arXiv:1303.4415] [INSPIRE].
J. Ecker, G. Honecker and W. Staessens, D6-brane model building on ℤ2 × ℤ6 : MSSM-like and left-right symmetric models, Nucl. Phys. B 901 (2015) 139 [arXiv:1509.00048] [INSPIRE].
J.P. Derendinger, S. Ferrara, C. Kounnas and F. Zwirner, On loop corrections to string effective field theories: Field dependent gauge couplings and σ-model anomalies, Nucl. Phys. B 372 (1992) 145 [INSPIRE].
G. Lopes Cardoso and B.A. Ovrut, A Green-Schwarz mechanism for D = 4, N = 1 supergravity anomalies, Nucl. Phys. B 369 (1992) 351 [INSPIRE].
G. Lopes Cardoso and B.A. Ovrut, Coordinate and Kähler σ-model anomalies and their cancellation in string effective field theories, Nucl. Phys. B 392 (1993) 315 [hep-th/9205009] [INSPIRE].
L.E. Ibáñez and D. Lüst, Duality anomaly cancellation, minimal string unification and the effective low-energy Lagrangian of 4-D strings, Nucl. Phys. B 382 (1992) 305 [hep-th/9202046] [INSPIRE].
L.E. Ibáñez, R. Rabadán and A.M. Uranga, σ-model anomalies in compact D = 4, N = 1 type IIB orientifolds and Fayet-Iliopoulos terms, Nucl. Phys. B 576 (2000) 285 [hep-th/9905098] [INSPIRE].
L.E. Ibáñez and G.G. Ross, Discrete gauge symmetry anomalies, Phys. Lett. B 260 (1991) 291 [INSPIRE].
L.E. Ibáñez and G.G. Ross, Discrete gauge symmetries and the origin of baryon and lepton number conservation in supersymmetric versions of the standard model, Nucl. Phys. B 368 (1992) 3 [INSPIRE].
T. Banks and M. Dine, Note on discrete gauge anomalies, Phys. Rev. D 45 (1992) 1424 [hep-th/9109045] [INSPIRE].
L.E. Ibáñez, More about discrete gauge anomalies, Nucl. Phys. B 398 (1993) 301 [hep-ph/9210211] [INSPIRE].
J.M. Frere, D.R.T. Jones and S. Raby, Fermion Masses and Induction of the Weak Scale by Supergravity, Nucl. Phys. B 222 (1983) 11 [INSPIRE].
J.A. Casas, A. Lleyda and C. Muñoz, Strong constraints on the parameter space of the MSSM from charge and color breaking minima, Nucl. Phys. B 471 (1996) 3 [hep-ph/9507294] [INSPIRE].
W.G. Hollik, A new view on vacuum stability in the MSSM, JHEP 08 (2016) 126 [arXiv:1606.08356] [INSPIRE].
A. Font and J.A. Lopez, Strings on eight-orbifolds, Nucl. Phys. B 703 (2004) 177 [hep-th/0405151] [INSPIRE].
S. Sethi, C. Vafa and E. Witten, Constraints on low dimensional string compactifications, Nucl. Phys. B 480 (1996) 213 [hep-th/9606122] [INSPIRE].
K. Dasgupta and S. Mukhi, A note on low dimensional string compactifications, Phys. Lett. B 398 (1997) 285 [hep-th/9612188] [INSPIRE].
S. Förste and D. Ghoshal, Strings from orientifolds, Nucl. Phys. B 527 (1998) 95 [hep-th/9711039] [INSPIRE].
S. Schäfer-Nameki and T. Weigand, F-theory and 2d (0, 2) theories, JHEP 05 (2016) 059 [arXiv:1601.02015] [INSPIRE].
F. Apruzzi, F. Hassler, J.J. Heckman and I.V. Melnikov, UV Completions for Non-Critical Strings, JHEP 07 (2016) 045 [arXiv:1602.04221] [INSPIRE].
T. Weigand and F. Xu, The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0, 2) F-theory Vacua, JHEP 04 (2018) 107 [arXiv:1712.04456] [INSPIRE].
L. Álvarez-Gaumé and E. Witten, Gravitational Anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
L. Lewin, Polylogarithms and Associated Functions, Elsevier Science Ltd, (1981).
B.C. Berndt, Ramanujan Notebooks Part II, chapter 14, eq. (25.1), Springer (1989)
L. Aparicio, D.G. Cerdeño and L.E. Ibáñez, A 119-125 GeV Higgs from a string derived slice of the CMSSM, JHEP 04 (2012) 126 [arXiv:1202.0822] [INSPIRE].
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Gonzalo, E., Herráez, A. & Ibáñez, L.E. AdS-phobia, the WGC, the Standard Model and Supersymmetry. J. High Energ. Phys. 2018, 51 (2018). https://doi.org/10.1007/JHEP06(2018)051
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DOI: https://doi.org/10.1007/JHEP06(2018)051