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Physics › Particle Physics

Extra Dimensions

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1,271prerequisites beneath it
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extra-dimensions kaluza-klein add-model randall-sundrum

Core Idea

Extra spatial dimensions beyond the three we observe could resolve the hierarchy problem by lowering the fundamental gravitational scale from the Planck mass to the TeV scale. In the ADD (Arkani-Hamed, Dimopoulos, Dvali) model, gravity spreads into large extra dimensions, diluting its apparent strength. In the Randall-Sundrum model, a warped extra dimension generates the hierarchy through an exponential factor. Both scenarios predict signatures at colliders and in gravitational experiments.

Explainer

Extra dimensions have been a recurring idea in theoretical physics since Kaluza and Klein proposed in the 1920s that electromagnetism could be understood as gravity in a fifth dimension. Modern extra dimension models, developed in the late 1990s, aim to solve the hierarchy problem -- why gravity is so much weaker than the other forces -- by changing the geometry of spacetime at short distances.

The ADD (large extra dimensions) model proposes that gravity propagates in 4 + n dimensions while the Standard Model particles are confined to a 4D brane. Gravity appears weak in 4D because its field lines spread into the extra dimensions, diluting the force. The fundamental gravitational scale M_D can be as low as ~1 TeV if the extra dimensions are large enough: for n = 2, R ~ 1 mm; for n = 6, R ~ 10 fermi. Collider signatures include: (1) direct graviton production (pp -> jet + graviton, where the graviton escapes into the extra dimensions, producing mono-jet + missing energy), (2) virtual graviton exchange enhancing dijet, dilepton, or diphoton production at high invariant mass, and (3) microscopic black hole production if the collision energy exceeds M_D.

The Randall-Sundrum model uses a single extra dimension with a warped (anti-de Sitter) geometry. The metric is ds2 = e-2k|y| eta_{mu nu} dxmu dxnu - dy2, where y is the coordinate of the extra dimension and k is the AdS curvature scale. The exponential warp factor generates the hierarchy between the Planck scale and the TeV scale without large extra dimensions: the extra dimension need be only ~10 Planck lengths in size. The Kaluza-Klein excitations of the graviton appear as spin-2 resonances at the TeV scale, with couplings suppressed by the TeV scale rather than the Planck scale. These resonances would appear as narrow peaks in the dilepton or diphoton invariant mass spectrum at the LHC.

Beyond the specific models, extra dimensions have had a profound influence on theoretical physics. The AdS/CFT correspondence relates the RS model to a dual description in terms of a strongly coupled 4D conformal field theory. This connection has been applied to model building (composite Higgs models as dual descriptions of RS models), to heavy-ion physics (using AdS/CFT to compute transport properties of the quark-gluon plasma), and to condensed matter physics. The phenomenology of extra dimensions also pioneered many experimental techniques now used more broadly: monojet searches, resonance searches in clean channels, and sensitivity to virtual effects of heavy new states.

Practice Questions 3 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → One-to-One Correspondence → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Making 10 as an Addition Strategy → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Iterated Integrals and Fubini's Theorem → Double Integrals in Cartesian Coordinates → Double Integrals in Polar Coordinates → Double Integrals in Polar Coordinates → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → The Measurement Problem → Interpretations of Quantum Mechanics → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Statistical Mechanics: Ensembles and the Boltzmann Distribution → Partition Function: Definition and Properties → Helmholtz Free Energy → Gibbs Free Energy → Phase Transitions: First Order and Second Order → Critical Phenomena and Critical Exponents → Landau Theory of Phase Transitions → Symmetry Breaking and Phase Transitions → Goldstone's Theorem and Gapless Modes → Goldstone Theorem → Higgs Mechanism → Electroweak Unification → Standard Model Overview → Collider Physics Methods → Cross Section Measurements → Higgs Boson Discovery and Properties → Beyond Standard Model (BSM) Overview → Extra Dimensions

Longest path: 191 steps · 1271 total prerequisite topics

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Beyond Standard Model (BSM) Overviewhard Standard Model Overviewhard

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