Introduction to String Theory & AdS/CFT

Justin FrantzNuclear 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 QMLocation fuzzyGR 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 – 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 provenWhy 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