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An Introduction to Extra Dimensions and String Phenomenology

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An Introduction to Extra Dimensions and String Phenomenology An introduction to extra dimensions and string phenomenology I. Antoniadis Albert Einstein Center, Bern University and LPTHE, UPMC/CNRS, Paris Summer School and Workshop on the Standard Model and Beyond Corfu, Greece, 1-11 September 2015 I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 1 / 66 Outline 1 Physical context and motivations 2 High string scale - heterotic string 3 High string scale - type II and D-branes 4 Low string scale and large extra dimensions 5 Experimental predictions I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 2 / 66 Bibliography An Introduction to perturbative and nonperturbative string theory Ignatios Antoniadis, Guillaume Ovarlez e-Print: hep-th/9906108 Topics on String Phenomenology I. Antoniadis e-Print: arXiv:0710.4267 [hep-th] String theory in a nutshell E. Kiritsis Princeton University Press, 2007 String theory and particle physics: An introduction to string phenomenology Luis E. Ibanez, Angel M. Uranga Published in Cambridge, UK: Univ. Pr. (2012) 673 p I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 3 / 66 Fundamental interactions force range intensity of 2 protons intensity at 10−16 cm Gravitation 10−38 10−30 ∞ Electromagnetic 10−2 10−2 ∞ Weak 10−15 cm 10−5 10−2 (radioactivity β) Strong 10−12 cm 1 10−1 (nuclear forces) At what distance, gravitation becomes comparable to the other interactions? Planck length: 10−33 cm MPlanck 1015 the LHC energy! → ≃ × I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 4 / 66 Newton’s law 2 m −1/2 19 m r m Fgrav = GN G = MPlanck = 10 GeV • ←− −→ • r 2 N e2 Compare with electric force: F = => el r 2 2 2 effective dimensionless coupling GN m or in general GN E at energies E 2 Fgrav GN mproton −40 E m [17] = proton => = 2 10 Fel e ≃ => Gravity is very weak ! I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 5 / 66 Standard Model of electroweak + strong forces Quantum Field Theory Quantum Mechanics + Special Relativity Principle: gauge invariance U(1) SU(2) SU(3) × × Very accurate description of physics at present energies 17 parameters 1 mediators of gauge interactions (vectors): photon, W ±, Z + 8 gluons 2 matter (fermions): (leptons + quarks) 3 × electron, positron, neutrino (up, down) 3 colors 3 Higgs sector: new scalar(s) particle(s) I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 6 / 66 Electroweak symmetry : spontaneously broken ± 0 SU(2) U(1) U(1)photon => W , Z massive, photon massless × → տ observed at LEP a new particle is needed : Higgs boson (scalar) break the EW symmetry at 100 GeV ∼ generate mass for all elementary particles through their interaction with the Higgs field Englert-Brout-Higgs mechanism Englert-Brout; Higgs; Guralnik-Hagen-Kibble ’64 Its discovery was one of the main goals of LHC I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 7 / 66 Beyond the Standard Model : Why? to include gravity in a consistent quantum theory longstanding dream of unification of all fundamental forces of Nature origin of electroweak (EW) symmetry breaking what is behind the Brout-Englert-Higgs mechanism? hierarchy of masses and force intensities EW/gravity 1032 ∼ stability at the quantum level => fine-tuning of parameters in 32 decimal places! neutrino masses and oscillations origin of Dark Matter in the Universe I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 8 / 66 String theory: Quantum Mechanics + General Relativity point particle extended objects → • → particles string vibrations ≡ - quantum gravity - framework of unification of all interactions - “ultimate” theory: ultraviolet finite · no free parameters · mass scale (tension): Mstring size: lstring ↔ rigid string : known particles (massless) vibrations : infinity of massive particles I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 9 / 66 Strings and extra dimensions Consistent theory 9 spatial dimensions ! ⇒ six new dimensions of space matter and gauge interactions may be localized in less than 9 dimensions => our universe on a membrane ? [14] p-plane: extended in p spatial dimensions p = 0: particle, p = 1: string,. I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 10 / 66 Extra Dimensions how they escape observation? finite size R Kaluza and Klein 1920 energy cost to send a signal: E > R−1 compactification scale ← experimental limits on their size light signal E > 1 TeV ⇒ ∼ R < 10−16 cm ∼ how to detect their existence? motion in the internal space => mass spectrum in 3d I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 11 / 66 Dimensions D=?? I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 12 / 66 example: - one internal circular dimension - light signal 5 plane waves eipy periodic under y y + 2πR → n => quantization of internal momenta: p = R ; n = 0, 1, 2,... => 3d: tower of Kaluza Klein particles with masses Mn = n/R 2 p2 ~p2 p2 =0 => p2 = p2 = n 0 − − 5 5 R2 E >> R−1 : emission of many massive photons propagation in the internal space [10] ⇔ I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 13 / 66 Our universe on a membrane Two types of new dimensions: longitudinal: along the membrane • transverse: “hidden” dimensions • only gravitational signal => R⊥ < 1 mm ! ∼ I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 14 / 66 Adelberger et al. ’06 R⊥ < 45 µm at 95% CL ∼ dark-energy length scale 85µm • ≈ I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 15 / 66 Low scale gravity Extra large dimensions can explain the apparent weakness of gravity ⊥ total force = observed force volume × ⊥ total force (1) at 1 TeV n dimensions of size R ≃ O ⊥ n = 1 : R 108 km excluded ⊥ ≃ n = 2 : R 0.1 mm (10−12 GeV) ⊥ ≃ possible n = 6 : R 10−13 mm (10−2 GeV) ⊥ ≃ distances > R : gravity 3d • ⊥ however for < R⊥ : gravity (3+n)d strong gravity at 10−16 cm 103 GeV • ↔ 30 10 times stronger than thought previously! [19] I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 16 / 66 Low scale gravity Extra large dimensions can explain the apparent weakness of gravity ⊥ total force = observed force volume [5] × ⊥ ↑ ↑ ↑ ∗ 2+n 2 n G E = GN E V E N × ⊥ ∗ −(2+n) GN = M∗ : (4+ n)-dim gravitational constant total force (1) at 1 TeV n dimensions of size R ≃ O ⊥ n => V⊥ = R⊥ => M2 = M2+nRn for M 1 TeV => (R M )n 1032 P ∗ ⊥ ∗ ≃ ⊥ ∗ ∼ I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 17 / 66 Gravity modification at submillimeter distances Newton’s law: force decreases with area 3d: force 1/r 2 ∼ (3+n)d: force 1/r 2+n ∼ 4 observable for n = 2: 1/r with r << .1 mm [16] I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 18 / 66 Connect string theory to the real world Is string theory a tool for strong coupling dynamics or a theory of fundamental forces? If theory of Nature can string theory describe both particle physics and cosmology? I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 19 / 66 At what energies strings may be observed? Very different answers depending mainly on the value of the string scale Ms 18 −32 Before 1994: Ms MPlanck 10 GeV ls 10 cm After 1994: ≃ ∼ ≃ - arbitrary parameter : Planck mass MP TeV −→ - physical motivations => favored energy regions: ∗ 18 MP 10 GeV Heterotic scale High : ≃ 16 ( MGUT 10 GeV Unification scale ≃ 11 2 Intermediate : around 10 GeV (M /MP TeV) s ∼ SUSY breaking, strong CP axion, see-saw scale Low : TeV (hierarchy problem) I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 20 / 66 High string scale perturbative heterotic string : the most natural for SUSY and unification gravity and gauge interactions have same origin massless excitations of the closed string But mismatch between string and GUT scales: 2 Ms = gH MP 50 M GUT g α GUT 1/25 [35] ≃ H ≃ ≃ 2 in GUTs only one prediction from 3 gauge couplings unification: sin θW introduce large threshold corrections or strong coupling Ms M GUT → ≃ but loose predictivity [24] I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 21 / 66 Heterotic string gravity + gauge kinetic terms [36] 1 1 [d 10x] M8 (10) + [d 10x] M6 2 simplified units: 2 = π =1 g 2 H R g 2 H FMN Z H Z H Compactification in 4 dims on a 6-dim manifold of volume V6 => V V [d 4x] 6 M8 (4) + [d 4x] 6 M6 2 g 2 H R g 2 H Fµν Z H Z H ||2 || 2 MP 1/g => 1 1 1 M2 M2 V M6 M gM g g√V M3 P = 2 H 2 = 2 6 H => H = P H = 6 H g g gH gH < 1=> V6 string size ∼ ∼ I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 22 / 66 GUT prediction of QCD coupling 2 input αem, sin θW => output α3 [36] exp value → I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 23 / 66 Heterotic string: Spectrum Gauge group G affine current algebra in the R-movers (bosonic) CFT ↔ a b abc c ab Jn , Jm = f Jn+m + kG δ δn+m kG : integer level of central extension h 2 i 2 gG = gH /kG · => kG = 1 : dims of allowed matter reps constrained by kG ) · simplest constructions (CY’s, orbifolds, lattices, free fermions) maximum rank: 22 guarantee gauge coupling unification at MH allowed reps: fundamentals & 2-index antisym of unitary groups, spinors of orthogonal groups However: - no adjoints to break GUT groups 2 - in SM sin θW = 3/8=> fractional electric charges Schellekens ’90 I. Antoniadis (Corfu School 2015) Extra dimensions and string phenomenology 24 / 66 (Hyper)charge quantization All color singlet states have integer charges fractional electric charged states: nice prediction or problematic? lightest is stable => problematic? ways out: - superheavy + inflate away - be confined to integrally charged by extra gauge group live without adjoints => non conventional ‘semi’-GUTs e.g.
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