An Introduction to Extra Dimensions and String Phenomenology

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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