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Introduction to String Theory & AdS/CFT

Introduction to String Theory & AdS/CFT. From a non-expert!!!!. Justin Frantz Nuclear Lunch 09/09/09. Introduction. String Theory is not just one theory but has evolved into a both a set of theories set of techniques

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Introduction to String Theory & AdS/CFT

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

  2. 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…

  3. 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

  4. Standard Model and QCD Microscopically includes the what the forces act upon…. • 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

  5. 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 Photon fermion-- 4 spinor dimensions 4 spacial dimensions

  6. 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 • http://online.kitp.ucsb.edu/online/plecture/witten/

  7. 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

  8. 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

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

  10. Dam Thanh Son Talk:

  11. 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…

  12. 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

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