Introduction to String Theory

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 EM 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 -- 2gt state (uses
  creation anniliation operators like for the QM
  Simple Harmonic Oscillator)
• Perturbation Theory Power Series of more and
  more complicated transitions (2-gt2, 2-gt3 )
  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
• Ive heard can do pages and pages of calcs in
  his head
• Downloading from the Mothership
• Nice simple introduction/presentation at
• http//online.kitp.ucsb.edu/online/plecture/witten
  /

7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
String Theory

• Currently need gt 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 dont
• 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

11
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

12
Dam Thanh Son Talk
A field theory much like QCD? Strongly
Coupled Problem no confinement though
13
Dam Thanh Son Talk
14
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
15
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/ dataamong 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