String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 - PowerPoint PPT Presentation

String Theory in the LHC Era J Marsano (marsano@uchicago.edu) 1 Tuesday, July 10, 12

String Theory in the LHC Era 5. Physics Beyond the Standard Model 1. Electromagnetism and and Supersymmetry (4/28) Special Relativity (3/31) 6. Einstein’s Gravity (5/5) 2. The Quantum World (4/7) 7. Why is Quantum Gravity so Hard? 3. Why do we need the Higgs? (4/14) (5/12) 4. The Standard Model (4/21) 8. String Theory (5/19) 9. String Theory and Our World (6/2) No lecture on Memorial Weekend (5/26)! 2 Tuesday, July 10, 12

Why is Quantum Gravity so hard? No clean separation between physics at large distances (which we directly measure) and physics at short distances Quantum gravity is very sensitive Quantum effects can become to short distance physics important at large distance scales 3 Tuesday, July 10, 12

Why is Quantum Gravity so hard? Plan: g µ ν g µ ν g µ ν 2. Black Hole 1. Graviton exchange Information Paradox 4 Tuesday, July 10, 12

g µ ν g µ ν g µ ν 1. Graviton exchange 5 Tuesday, July 10, 12

Gravity Curvature of spacetime by energy-momentum Gravity waves ↔ ‘ripples of spacetime like electromagnetic waves Can we describe quantum gravity like quantum electromagnetism? 6 Tuesday, July 10, 12

Electromagnetic Wave ‘carrier’ of electromagnetism e − This electron doesn’t feel any change in force until the electromagnetic waves get here → information doesn’t travel faster than light! e − 7 Tuesday, July 10, 12

Quantum Electrodynamics Force mediated by exchange of ‘smallest piece’ of an Julian Richard Sin-Itiro Schwinger Feynman Tomonoga electromagnetic wave: a photon Fundamental interaction: γ electron-photon coupling e − e − γ e − e − e − e − 8 Tuesday, July 10, 12

Quantum Electrodynamics To compute anything, we must ‘sum over histories’ Julian Richard Sin-Itiro Schwinger Feynman Tomonoga γ γ γ + = e − e − e − e − e − e − γ Coupling of electron with photon e − e − + ... + 9 Tuesday, July 10, 12

γ γ γ + = e e − e − e − e − e − e − e e e Coupling of electron γ with photon e − e − + e + ... e e e e = e + ( . . . ) e 3 + ( . . . ) e 5 + . . . Fortunately our expansion parameter is small but... e 10 Tuesday, July 10, 12

γ γ γ + = e e − e − e − e − e − e − e e e Coupling of electron γ with photon e − e − + e + ... e e e e = e + ( . . . ) e 3 + ( . . . ) e 5 + . . . Fortunately our expansion parameter is small but... e Infinity! 10 Tuesday, July 10, 12

γ γ γ + = e e − e − e − e − e − e − e e Coupling of electron γ with photon e − e − + e + ... e e Infinity! e e Infinity from very high energy particles in loops Occurs because we don’t really know how to describe high energy/short distance physics Our only recourse is to parametrize our ignorance 11 Tuesday, July 10, 12

Introduce new interactions γ γ + e − e − e − e − Represents short distance physics that we don’t understand 12 Tuesday, July 10, 12

Introduce new interactions γ γ + e − e − e − e − Represents short distance physics that we don’t understand 12 Tuesday, July 10, 12

Introduce new interactions e − e − e − e − + γ γ + e − e − e − e − Represents short distance physics that we don’t understand + γ γ γ γ 12 Tuesday, July 10, 12

Contributions from our new interactions γ γ γ + = e − e − e − e − e − e − γ γ Coupling of electron + ... with photon + + e − e − e − e − e + ( . . . ) e 3 + ( . . . ) e 5 + . . . = Finite! 13 Tuesday, July 10, 12

With our 3 new interactions, everything is finite! γ γ e − e − e − e − + + e − e − e − e − + γ γ γ γ Represents short distance physics that we don’t understand Sensitive to short distance physics Miracle of Quantum Electrodynamics: through only 3 numbers! Only 2 are observable: Electron charge and mass Once we measure two things, Quantum Electrodynamics can crank out predictions 14 Tuesday, July 10, 12

Infinities everywhere! Standard Model depends on many details of short distance physics Miracle of the Depends on short distance physics Standard Model: only through 19 parameters (particle masses and couplings) 15 Tuesday, July 10, 12

What about Gravity? 16 Tuesday, July 10, 12

g µ ν F = Gm 1 m 2 1 r 2 G ∼ M 2 Planck e − e − M Planck ∼ 10 18 GeV Strength of gravitational interaction has ‘units’ Characteristic energy scale -- first sign of trouble ...we’ve seen this before... 17 Tuesday, July 10, 12

p + 1 e − G F ∼ (300 GeV) 2 n Fermi constant ν e Enrico Fermi Fermi’s theory of beta decay also had a characteristic energy scale Computations in this ( . . . )( G F E 2 ) + ( . . . )( G F E 2 ) 2 + . . . theory look like Expansion parameter is dimensionless (a number with no units) 18 Tuesday, July 10, 12

p + 1 e − G F ∼ (300 GeV) 2 n Fermi constant ν e Enrico Fermi Fermi’s theory of beta decay also had a characteristic energy scale Computations in this ( . . . )( G F E 2 ) + ( . . . )( G F E 2 ) 2 + . . . theory look like ◆ 2 ◆ 4 ✓ ✓ E E = ( . . . ) + ( . . . ) + . . . 300 GeV 300 GeV Expansion parameter is dimensionless (a number with no units) Trouble for energies E much bigger than 300 GeV 18 Tuesday, July 10, 12

p + 1 e − G F ∼ (300 GeV) 2 n Fermi constant ν e Trouble for energies E much bigger Enrico Fermi than 300 GeV p + New physics emerged around 300 GeV M W ∼ 80 GeV n W − Fermi’s theory an ‘effective theory’ e − that can only describe physics below 300 GeV ν e 19 Tuesday, July 10, 12

g µ ν 1 G ∼ M 2 Planck Gravity is similar M Planck ∼ 10 18 GeV e − e − g µ ν g µ ν g µ ν Coupling of electron = with graviton + e − e − e − e − e − e − ◆ 2 ◆ 4 ✓ ✓ E E ( . . . ) + ( . . . ) M Planck M Planck + ... 20 Tuesday, July 10, 12

g µ ν 1 G ∼ M 2 Planck Gravity is similar M Planck ∼ 10 18 GeV e − e − g µ ν g µ ν g µ ν Coupling of electron = with graviton + e − e − e − e − e − e − ◆ 2 ◆ 4 ✓ ✓ E E ( . . . ) + ( . . . ) M Planck M Planck + ... Infinity! 20 Tuesday, July 10, 12

Two (not unrelated) problems g µ ν g µ ν g µ ν = + + ... e − e − e − e − e − e − ◆ 2 ◆ 4 ✓ ✓ E E ( . . . ) + ( . . . ) M Planck M Planck Infinity! 1. Expansion breaks down at 2. Infinities again! energies close to M Planck Sensitivity to unknown → this is an ‘effective theory’ at best short distance physics New physics must be Can try to parametrize waiting at M Planck our ignorance again... 21 Tuesday, July 10, 12

Infinities in Quantum Gravity Let’s add new local interactions to model short distance physics g µ ν g µ ν g µ ν g µ ν ...must be missing some physics This is infinite model with new interaction 22 Tuesday, July 10, 12

Infinities in Quantum Gravity Let’s add new local interactions to model short distance physics g µ ν g µ ν g µ ν g µ ν ...must be missing some physics This is infinite model with new interaction g µ ν g µ ν ...must be missing g µ ν g µ ν g µ ν g µ ν some physics This is still infinite model with another new interaction 22 Tuesday, July 10, 12

Infinities in Quantum Gravity Let’s add new local interactions to model short distance physics g µ ν g µ ν g µ ν g µ ν ...must be missing some physics This is infinite model with new interaction g µ ν g µ ν ...must be missing g µ ν g µ ν g µ ν g µ ν some physics This is still infinite model with another new interaction g µ ν g µ ν g µ ν g µ ν ...must be missing some physics g µ ν g µ ν g µ ν g µ ν model with another new interaction This is still infinite 22 Tuesday, July 10, 12

Infinities in Quantum Gravity Let’s add new local interactions to model short distance physics g µ ν g µ ν g µ ν g µ ν ...must be missing some physics This is infinite model with new interaction g µ ν g µ ν ...must be missing g µ ν g µ ν g µ ν g µ ν This process never ends! some physics This is still infinite model with another new interaction g µ ν g µ ν g µ ν g µ ν ...must be missing some physics g µ ν g µ ν g µ ν g µ ν model with another new interaction This is still infinite 22 Tuesday, July 10, 12

Infinities in Quantum Gravity Let’s add new local interactions to model short distance physics We need to introduce INFINITELY MANY new parameters! g µ ν g µ ν g µ ν g µ ν g µ ν + + + ... g µ ν g µ ν g µ ν g µ ν Unlike the Standard Model, gravity is very sensitive to the details of short distance physics Must make infinitely many measurements before we can predict anything! 23 Tuesday, July 10, 12

g µ ν g µ ν g µ ν g µ ν g µ ν + + + ... g µ ν g µ ν g µ ν g µ ν We cannot cleanly separate long and short distance physics like we did with the Standard Model 24 Tuesday, July 10, 12