Introduction to String Theory & AdS/CFT Justin Frantz Nuclear Lunch 09/09/09 From a non-expert!!!!

Introduction String Theory is not just one theory but has evolved into a both a set of theories set of techniques AdS/CFT is one such sub-theory/technique that has recently found an application to Physics of the Strong Force This week: start w/ general intro to String Theory – Next week discuss AdS/CFT again in more detail…

Forces and General Relativity Four Forces: Electromagnetic,Weak, Strong, Gravity – In fact EM & Weak are currently fully unified as one theory (one force) Both E&M and Gravity follow inverse square laws to good approximation – Current understanding: “accident” First, Gravity is best explained (on large length scales) by General Relativity LHS Curvature of space-time itself (R == Ricci Tensor) RHS Presence of Matter/Energy (T = Energy/Mom Tensor) Form of matter not specified

Standard Model and QCD Standard model particles Hadrons QED-ElectroWeak, QCD: Quantum field theories – Using Perturbation Theory Approximation Strong Force – Quantum ChromoDynamics – Confinement/ Asymptotic Freedom – Low energy QCD  Perturbation theory fails: “uncalculable” – Not motivation for String Theory itself but is motivation for use of AdS/CFT Notice that Gravity is absent: – However, SM “proposes” the existence of the mediator graviton which couples w/ all particles – Does not specifiy any details Microscopically includes the what the forces act upon….

Quantum Field Theory/GR Quantum Field Theory – Particles (e.g. electrons) and Forces (via “mediating particles” e.g. photons) treated “equally” as fields – Quantized: 2 electrons -- |2> state (uses creation anniliation operators like for the QM Simple Harmonic Oscillator) – Perturbation Theory: Power Series of more and more complicated transitions (2- >2, + 2->3+ …) sum to “total probability”  more complicated less important Because of Uncertainty Principle implied by QM  Location fuzzy  GR Curvature goes “haywire” – So GR and QFT are not compatible w/ current formulations QED Lagrangian fermion-- 4 spinor dimensions 4 spacial dimensions Photon

String Theory Edward Witten – Intellectual Leader of String Theory – Regarded by some as “Einstein” or our generation – I’ve heard: can do pages and pages of calc’s in his head – “Downloading from the Mothership” Nice simple introduction/presentation at –

String Theory Currently need >= 10 dimensions (9 space 1 time) to fit all SM particles, including new “SuperSymmetric” SUSY particles ~6 different versions of the theory SUSY solves Hierarchy Problem : -Why is Gravity so weak (vs 3 other Forces)? Compactification: why we don’t see the other dimensions M-theory : Witten discovered one 11-D theory which includes others strings  branes Duality / Holographic Principle Recent Advancement leading to recent AdS/CFT activity and other things – Like Gauss’ Law or Curl Theorem: – All information in any volume (n-D space) is reflected on the surface of that volume E.g. all interactions reflected on surface as some kind of fluctuation on that surface. – Theory of the volume and theory of the surface same mathematical object

Basic Idea For “AdS/CFT” Certain configuration in Higher Dimensional “AdS” Space dual to a Quantum (Conformal) Field Theory on some surface in that space Some complicated Field theory calculations become simple “geometric’ problems in higher dimensions

Dam Thanh Son Talk: A field theory much like QCD  Strongly Coupled Problem: no confinement though

Dam Thanh Son Talk:

Reminder: still just a hypothesis  Not proven Why is it useful?  At minimum can provide insights about which directions to take field theory calc  benefit from the field theory calc…

Results For Heavy Ions, where we think we create a hot plasma of raw QCD fields w/ very low viscosity – e.g. has yielded a conjectured lower bound for the viscosity of ANY quantum fluid that is compatible w/ data…among many other calculations Easy way to calculate energy loss of certain (heavy) quarks in strongly coupled quantum medium – Some predictions that can be tested! Has also been applied to models of hadrons