1、String Theory:A Status ReportFoundations of Modern Physics Quantum Theory Special Relativity General RelativityQuantum Mechanics+Special Relativity=Quantum Field TheoryThe standard model of particle physicsUnprecedented success!Adding Gravity/General RelativityMany problems arise:moonearthgravitongr
2、avitonelectron Quantum fluctuations are infinite!Gravity=General Relativity =Modification of space-timeThis is not merely a technical problembut a conceptual problem.We should not expect the quantization to be easy.Conceptual problems:The light-cone undergoes quantum fluctuations How to maintain cau
3、sality?Information loss in black holes(?)Is the theory unitary?The cosmological constant 10-120M4Planck Why so small?Calculate it.Cosmology,early Universe,inflation Wave function of the Universe Initial conditionsChallenge:Combine General Relativity with Quantum MechanicsString TheoryInvented in the
4、 late 60s as a theory of the strong interactions.Mid 70s:String theory is a theory of gravity!Gravity is not an option in string theory.It is a logical consequence of it!Main idea:the fundamental building blocks are not point-like particles but strings Their small size(10-33cm)makes them look point-
5、like.Different vibration modes of the string are different particles.electronquarkVery economical!The theory on the two-dimensional string world-sheet is reparametrization invariant(geometrical).String InteractionJoining and splitting First String Revolution The Perturbative era(Mid 80s-Mid 90s)Cons
6、istent perturbation expansion Several consistent string theories(type I,type IIA,type IIB,heterotic SO(32),heterotic E8xE8)String propagation in curved spaces Connection to conformal field theory The theory has many ground states characterized by the six dimensional compactification.Some of these gr
7、ound states are similar to our world(4 dimensions,electrons,photons,etc.).Experimental verification is not easy In order to see stringy phenomena we need a microscope with a resolution of 10-33cm.The resolution of the best available accelerators is only 10-16cm.Indirect experimental confirmation is
8、needed!Second String RevolutionThe Non-perturbative era(Mid 90s-?)Exact results using the magic of supersymmetry Extended objects Large extra dimensions Non-commutative geometry String duality String theory is unique Black hole information puzzle Many“ground states”p-branes:0-brane=particle1-brane=s
9、tring2-brane=membrane etc.The theory has extended objects like membranesSome of them are regions where strings can end:D-branes(Dirichlet branes)Non-Commutative GeometrySometimes the space-time coordinates on the D-brane do not commute x,y 0(Like electrons in the first Landau level.)New connections
10、to mathematics.Extra DimensionsIn addition to the three space dimensions there can be more“invisible dimensions”Small“invisible dimensions”(Kaluza Klein)Large“invisible dimensions”(brane world)Large“invisible dimensions”brane world Our four space-time dimensionsWe are trapped in a brane and cannot“s
11、ee”the other dimensions.Gravity is weak because the extra dimensionsare large.ExtradimensionsString Duality:The underlying space-time on which the strings propagate is ambiguousWe cannot tell whether strings propagate onor This duality generalizes:E B duality in electromagnetism P Q“duality”in quant
12、um mechanics Order disorder duality in Ising modelTelling the same story in different languages.Duality exchanges strong coupling weak coupling All p-branes are equally fundamental.String theory is not a theory of strings!String duality exchanges the different branesMap of the ground states of strin
13、g theorytype I type IIAtype IIBheterotic E8xE8heterotic SO(32)11 dim.ground stateWe are hereAll previously known theories are now understood as different descriptions of the same theory.String duality exchanges them.Telling the same story in different languages.The theory is unique!Some details“Fund
14、amental objects”at one end are composites elsewhere Weak coupling at one end corresponds to strong coupling at another end The extrapolation from end to end uses the magic of supersymmetry The theory is inherently quantum mechanicalBlack hole information puzzleSuggestion:All the information about th
15、e interior of a black hole is summarized by the state of its surface,the horizon.Recent developments-Holography-show that in string theory(at least in certain situations)the state of the system is completely characterized by the behavior of its boundary.Strings in AdS=CFT on boundaryEntropy=AreaNo i
16、nformation loss in black holes=The Ground State(s)The recent advances have uncovered many new solutions of the equations of motion ground states Is the ground state selected by initial conditions connection to cosmology?If all these solutions are acceptable,do they exist elsewhere in the Universe An
17、thropic solution?Our understanding lacks a crucial ingredient.SummaryString theory is the only candidate for a complete theory of Nature.Ultimate confirmation of the theory will require verification by experiment.Its fundamental principles are not yet understood,but the past few years have seen tremendous progress:-Nonperturbative understanding-The theory is unique-Black holes-Connections with other branches of physics and mathematics
