Brane World

1. Brane World Cosmological ideas from string theory Cosmology String (M) theory The vacuum in particle physics Branes and brane world Problems in quantum gravity Holography

2. Cosmological Questions • What are space and time? • Why are there 3 spatial directions and 1 time? • How did the Universe begin? • How will the Universe end? • Why does it contain the sorts of matter it does? • How does that matter interact and produce galaxies etc? Very ambitious! – Physics has been very successful though so can begin to address these issues

3. The Big Bang In General Relativity space and time are dynamic – we believe we live in an expanding Universe • Explosion! - galaxies are moving apart • Flash – universe is full of remnant radiation • Smoke and Ash – correctly predict the abundances of H, He, Be…

4. Singular Beginning At very early times the whole Universe and contents squeezed into a tiny volume… Describe as a hot, dense soup of the fundamental building blocks of nature Observing the expansion we find it is slowing due to the gravitational attraction of matter Critical Ending It seems to be balanced between expanding forever and eventual collapse…. But then 90% of matter must be new DARK MATTER We need to know some particle physics!

5. The Particle World Forces • Electromagnetism • Strong nuclear • Weak nuclear • Gravity Particles 6 quarks 3 electrons 3 neutrinos

6. Quantum Rules of Motion Energy comes in lumps E = h f Fields can look like particles The photon is the quantum of the electromagnetic field/ light

7. Quantum Dynamics The quantum in some sense travels by both paths…. There is an uncertainty in the position and momentum of the quantum x p > h Heisenberg’s Uncertainty Principle t E > h Or equally

8. The Quantum Vacuum E t > h The vacuum can borrow energy for short periods E = mc 2 The borrowed energy can be used to create particles (You can’t just create an electron because of charge conservation - but can create electron positron pair) The quantum vacuum is a seething mass of particles appearing and disappearing constantly….

9. How Can You Tell? The “virtual” particle pairs interfere in electron scattering processes. The effective charge seen in two electron scattering depends on the separation of the electrons.

10. The Strong Nuclear Force The strong nuclear force is described by a theory that is similar to electromagnetism… except that the fields carry (colour) charge….. This difference changes the way in which the vacuum is polarized so that…

11. Confinement You can never pull hard enough to liberate a quark from a proton… The QCD Vacuum Every so often quantum effects create a quark anti-quark pair. The attractive force is so strong that binding energy >> mass energy The vacuum has lower energy if it fills itself with quark anti-quark pairs!

12. The vacuum is really full of quark anti-quark pairs with a density like that of an atomic nucleus (10 grams/cm ) !! 15 3 The Proton Mass The quark pairs are responsible for the proton’s mass Interaction energy provides proton mass

13. The Origin of Mass The strong nuclear force cannot explain the mass of the electron though… Or very heavy quarks such as the top quark top mass = 175 proton mass The Higgs Boson We suspect the vacuum is full of another sort of matter that is responsible – the higgs…. To explain the top mass the higgs vacuum must be 100 times denser than nuclear matter!!

14. Quantum Gravity If the vacuum is full of all this stuff shouldn’t we be pulled gravitationally by it? Since it is uniformily distributed there is no net pull (equal space to all sides) But General Relativity says the energy should uniformily curve space-time… the Universe should be the size of a grapefruit!! There’s something big we don’t understand about quantum gravity Gravity is so weak that we’ve never measured it’s effects between individual particles or on distance scales smaller than 1mm!

15. Gravity is different to the other forces – it’s only attractive… In General Relativity this shows up in that gravitational waves have different polarizations to electromagnetic waves What fundamental theory can encompass both types of fields?

16. String Theory String theory unifies gravity and other forces String theory is A quantum theory of gravity.. Is it THE quantum theory of gravity? - entering realm of speculation!

17. Extra Dimensions Surprisingly the mathematics of string theory only makes sense in 9 spatial dimensions and 1 time dimension! A prediction…. But wrong!! Compactification We can imagine a space where directions are curled up We study A string in this space not ALL the strings that make the space….Why are 6 dimensions compact… by what mechanism? UNKNOWN!

18. Shrinking Dimensions Away Remember particles are really quanta of fields… only very special field configurations make sense on a compact dimension Energy = E, 2E, 3E, 4E, 5E,…. As we shrink the circumference away E grows – eventually you can’t make the extra states… it’s gone! 19 Standard string lore – E is 10 proton mass

19. Wrapping Strings Closed strings can do something new in a compact space Wrapping modes have energies E’, 2E’, 3E’, 4E’, 5E’… As we shrink the circumference away these states are very low energy Dual Spatial Directions If we “confuse” winding modes and kinetic modes we can see a new dimension appear as another disappears!

20. Membranes Only closed strings see the new direction… not open strings… Electromagnetic particles live on a sub-space or “brane” “Existence proof” for such a world Gravitons live in a higher dimension “bulk”

21. Could Our Universe Be A Brane? The strength of gravity is determined by the number of spatial dimensions (gravitons spread out around mass) S U F = G M m 2 D=3+1 r 2 R p But…. we don’t know anything about gravity on length scales below 1mm… R could = 1mm… and we wouldn’t know it! If so we’ve miscalculated the strength of gravity (G) – it could become strong in our particle accelerators at any new energy!!

22. Matter Loss To The Bulk Our Universe will slowly lose matter into the bulk… In particle physics gravity is too weak to ever see these events In fact the energy loss from the centre of stars is too low to see too!

23. Other Branes Why should there be only one brane in the higher dimension spacetime? There could be entire Universes only mm away! The matter on the other brane will only interact with our world gravitationally – it’s dark matter…. W S E U N Until we can produce high energy gravitons that are strongly interacting there’s little way to directly probe this idea though

24. Brane Collisions There’s no reason branes should be static in the extra dimensions…. So they could collide! This would be catastrophic! Huge amounts of energy would be dumped into our Universe…. Could that have triggered the currently observed expansion of the Universe??!!

25. Holography General Relativity predicts there should be objects whose gravitational attraction is enough to stop even light escaping – BLACK HOLES ‘tHooft argued that any information dropped into a black hole must be • lost to our Universe • spread over the surface If the surface can contain all the information of the contents the real theory of the Universe must be 2 + 1 dimensional!

26. Strong Nuclear Force is Holographic String theory grew out of attempt to describe confined quarks The resulting string theory has recently been discovered to describe gravity in 4+1 dimensions! Is the real world holographic?? If there is only as much information in Universe as on surface problem of over density of vacuum material may be solved…??

27. Overview • The large scale structure of Universe was determined by particle interactions just after the Big Bang • Our theories of particles don’t fit with theories of gravity • String Theory is an attempt to construct a sensible theory of both • We are realizing it predicts wild possibilities • Extra dimensions and other Universes • Or are we a hologram in fewer dimensions? • Many exciting possibilities but very hard to experimentally test because gravity is very very weak….

28. M Theory If you study strings at scales where they look like particles you get a theory of particles… can construct these independently 10 dimensional theories naturally map on to strings There is an 11d theory that we now realize naturally maps onto membranes Compactifying gives string theory – fundamentally 11d?