Introduction to String Theory - Matthias...
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Universität Frankfurt, HGS-HIRe Powerweek, July 16-21st 2012
by Matthias Kaminski (University of Washington)
Introduction to String Theory
QFT Gravity
![Page 2: Introduction to String Theory - Matthias Kaminskimkaminski.people.ua.edu/uploads/8/1/1/7/81173116/power... · 2018-10-08 · Matthias Kaminski Introduction to String Theory Page 5](https://reader030.fdocuments.in/reader030/viewer/2022040215/5ecae4dd51cb2e6d7d6ee576/html5/thumbnails/2.jpg)
Universität Frankfurt, HGS-HIRe Powerweek, July 16-21st 2012
by Matthias Kaminski (University of Washington)
Introduction to String Theory
QFT Gravity
![Page 3: Introduction to String Theory - Matthias Kaminskimkaminski.people.ua.edu/uploads/8/1/1/7/81173116/power... · 2018-10-08 · Matthias Kaminski Introduction to String Theory Page 5](https://reader030.fdocuments.in/reader030/viewer/2022040215/5ecae4dd51cb2e6d7d6ee576/html5/thumbnails/3.jpg)
Superstring Theory
Universität Frankfurt, HGS-HIRe Powerweek, July 16-21st 2012
by Matthias Kaminski (University of Washington)
Introduction to String Theory
QFT Gravity
![Page 4: Introduction to String Theory - Matthias Kaminskimkaminski.people.ua.edu/uploads/8/1/1/7/81173116/power... · 2018-10-08 · Matthias Kaminski Introduction to String Theory Page 5](https://reader030.fdocuments.in/reader030/viewer/2022040215/5ecae4dd51cb2e6d7d6ee576/html5/thumbnails/4.jpg)
Matthias Kaminski Introduction to String Theory Page 2
Lecture I: Overview of String Theory & Applications
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Overview
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Overview
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Overview
What is string theory?
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Overview
What is string theory?String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity (invariance principles). It is a contender for a theory of everything, a self-contained mathematical model that describes all fundamental forces and forms of matter, a theory of strings, branes, and their dynamics.
Superstring Theory
QFT Generalrelativity
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OverviewStructure of string theory - limits & dualities
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Matthias Kaminski Introduction to String Theory Page 5
OverviewStructure of string theory - limits & dualities
supergravity theories are low-energy limits of these string theories (e.g. type IIA supergravity is derived from type IIA string theory by taking the massless tree-level approximation)
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Matthias Kaminski Introduction to String Theory Page 5
OverviewStructure of string theory - limits & dualities
supergravity theories are low-energy limits of these string theories (e.g. type IIA supergravity is derived from type IIA string theory by taking the massless tree-level approximation)
supergravity (SUGRA) emerges when making SUSY local
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Matthias Kaminski Introduction to String Theory Page 5
OverviewStructure of string theory - limits & dualities
supergravity theories are low-energy limits of these string theories (e.g. type IIA supergravity is derived from type IIA string theory by taking the massless tree-level approximation)
supergravity (SUGRA) emerges when making SUSY local
1+1 dim CFT on world-sheets of strings
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Matthias Kaminski Introduction to String Theory Page 5
OverviewStructure of string theory - limits & dualities
supergravity theories are low-energy limits of these string theories (e.g. type IIA supergravity is derived from type IIA string theory by taking the massless tree-level approximation)
supergravity (SUGRA) emerges when making SUSY local
1+1 dim CFT on world-sheets of strings
dualities relate these “corners of superstring theory”
T-duality
S-duality
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Terra incognita
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Terra incognita
M-theory
Type IIB
Type I
Type IIA
E8xE8heteroticstring
11-dim.SUGRA
SO(32)heteroticstring
Type IIB
SUGRA
Coastlines: SUGRA limits
Expeditions: string dualities
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OverviewModern research areas
conformal field theory (CFT)
integrability
applications to heavy-ion-collisions
dS/CFT
black holes, black branes
string phenomenology *
gauge/gravity correspondence (duality) *
AdS/CMT *
higher spin holography *
scattering amplitudes ** group projects
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OverviewAn eye on applications
MHV amplitudes
applications to heavy-ion-collisions
• shear viscosity over entropy density (hydro, dragging string)
• thermalization
• chiral magnetic effect chiral vortical effect
!
s=
1
4"(! = kB = c = 1) ! = lim
!!0![T xy, T xy]"(",k = 0)
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Matthias Kaminski Introduction to String Theory Page 8
OverviewAn eye on applications
MHV amplitudes
applications to heavy-ion-collisions
• shear viscosity over entropy density (hydro, dragging string)
• thermalization
• chiral magnetic effect chiral vortical effect
!
s=
1
4"(! = kB = c = 1) ! = lim
!!0![T xy, T xy]"(",k = 0)
![Page 19: Introduction to String Theory - Matthias Kaminskimkaminski.people.ua.edu/uploads/8/1/1/7/81173116/power... · 2018-10-08 · Matthias Kaminski Introduction to String Theory Page 5](https://reader030.fdocuments.in/reader030/viewer/2022040215/5ecae4dd51cb2e6d7d6ee576/html5/thumbnails/19.jpg)
Matthias Kaminski Introduction to String Theory Page
Monday, Tuesday, Thursday
09:00-10:00 Lecture
Break & Free discussion
10:30-11:30 Lecture
11:30-12:30 Hands-on tasksLunch
14:00-17:00 Hands-on tasks
17:00-19:00 Discussion of solutions
Wednesday, Friday: Group projects from 16:00-18:00
Saturday: Group projects discussion from 09:00-13:00
Monday, Tuesday: Visiting Strings2012 in München
Schedule
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Matthias Kaminski Introduction to String Theory Page
Lecture I: Overview of String Theory & Modern Research
(general relativity, action principles)
Lecture II: Bosonic String Theory(open/closed strings, quantization, string spectrum)
Lecture III: Bosonic String Theory(CFT, operator product expansion, Virasoro algebra, mode expansions, vertex operators)
Lecture IV: Bosonic String Theory(Polyakov path integral, string scattering amplitudes, string S-matrix)
Lecture V: Bosonic String Theory(compactification, moduli, spectrum)
Lectures
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Monday-Friday 9:00 - 10:00, 10:30 - 11:30
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Matthias Kaminski Introduction to String Theory Page
Lecture VI: Bosonic String Theory(one-loop amplitudes, T-duality, D-branes, outlook on superstrings)
Lecture VII: Superstring Theory(SUSY, type I, type II, Calabi-Yau compactification, T-duality, flux compactification, string geometry)
Lecture VIII: Superstring Theory(string dualities, M-theory, string phenomenology)
Lecture IX: Gauge/Gravity Duality & Black Holes(AdS/CFT conjecture, extensions)
Lecture X: Gauge/Gravity Duality & Black Holes(applications to heavy-ion collisions and cond-mat)
Lectures
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Monday-Friday 9:00 - 10:00, 10:30 - 11:30
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Matthias Kaminski Introduction to String Theory Page
Exercise I: General relativity, action principles, CFT
Exercise II: CFT, string scattering, string spectrum
Exercise III: Compactification, T-duality, spinors & SUSY
Exercise IV: Anomaly cancellation
Exercise V: AdS spacetime, correlation functions
Exercises
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Monday-Friday 11:30 - 17:00
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Matthias Kaminski Introduction to String Theory Page
Participants of the powerweek will
- be able to carry out simple computations in string theory
- have an overview of string theory basics & current string theory research
- know the origins of gauge/gravity duality
- have the knowledge needed to create simple string setups in order to investigate problems in current research
Goals
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Matthias Kaminski Introduction to String Theory Page
Blackboard
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Matthias Kaminski Introduction to String Theory Page
Invitation: Gauge/gravity correspondence
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-Why does it work?Stack of Nc D3-branes (coincident)
in 10 dimensions
near-horizon geometryAdS x S5
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D3 branes in 10d
duality
Two distinct ways to describe this stack:
4-dimensional worldvolume theory on the D3-branes
(e.g. Super-Yang-Mills)N = 4
(e.g. Supergravity)gauge side
gravity side
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Matthias Kaminski Introduction to String Theory Page
Invitation: Gauge/gravity correspondence
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-Why does it work?
Geometric setup: Strings/Branes
Find solutionconfiguration
Field Theory result
Stack of Nc D3-branes (coincident)in 10 dimensions
Add/change geometric objects on ‘gravity side’:
-How does it work?
near-horizon geometryAdS x S5
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D3 branes in 10d
duality
Two distinct ways to describe this stack:
4-dimensional worldvolume theory on the D3-branes
(e.g. Super-Yang-Mills)N = 4
(e.g. Supergravity)gauge side
gravity side
Example: Schwarzschild radius corresponds to temperature
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Matthias Kaminski Introduction to String Theory Page
Solutions(to some of the exercises)
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Matthias Kaminski Introduction to String Theory Page
Exercise 1.2
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Matthias Kaminski Introduction to String Theory Page
Solution to exercise 1.2 (1)
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Matthias Kaminski Introduction to String Theory Page
Solution to exercise 1.2 (2)
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Matthias Kaminski Introduction to String Theory Page
Solution to exercise 1.2 (3)
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Matthias Kaminski Introduction to String Theory Page
Solution to exercise 1.2 (4)
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Matthias Kaminski Introduction to String Theory Page
Exercise 2.1
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Matthias Kaminski Introduction to String Theory Page
Blackboard
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Matthias Kaminski Introduction to String Theory Page
Thanks to
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Martin Ammon (UCLA)Andreas Karch (UW)Maxwell T. Hansen (UW)John Fuini (UW)and the graduate students at UW