Transcript NuclearLunch_090909_AdSCFT

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
• 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
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
Quantum Field Theory/GR
• Quantum Field Theory
– Particles (e.g. electrons) and Forces (via “mediating particles” e.g. photons)
treated “equally” as fields
QED Lagrangian
Photon
fermion-- 4 spinor
dimensions
4 spacial
dimensions
– 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
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/
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:
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