String/M theory, MSc course, 7.5 p, Lp IV 2010
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Course codes: CTH: FFM 485 and GU: FY 4850
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Introductory meeting 2009: Tuesday, March 16, at 15.15 in Origo 6115
(the physics building called Origo, 6th floor, north wing).
Teacher: Professor Bengt E.W. Nilsson, phone 772 3160, Origo 6104C
Literature: "A first course in string theory", Barton Zwiebach,
(Cambridge university press 2004, 2nd ed.).
Available on the net and at Cremona.
Tentative study plan for the course:
week 1 (calender week 11): chapters 1-3, parts of chap 23
week 2 (calender week 12): chapters 4-6
Easter holiday (calender week 13)
week 3 (calender week 14): chapters 7-9
week 4 (calender week 15): chapters 10-12
week 5 (calender week 16): chapters 13-14
week 6 (calender week 17): parts of chapters 15-16
week 7 (calender week 18): chapters 17-19, (20), 21
week 8 (calender week 19): chapter 23
week 9 (calender week 20): examination (only on May 17-18)
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NEW Schedule: All lectures in Origo 6115
There will in general be TWO lectures each week. See the weekly schedule below for
which of the following times will be used
(Mondays at 15.15-17.00)
Tuesdays at 15.15-17.00
Thursdays at 10.00-11.45
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Additional reading:
Non-technical string literature:
An excellent popular account of the fundamental questions and
ideas of modern string/M theory can be found in
"The elegent universe", by Brian Greene (Jonathan Cape 1999).
Additional (more advanced) string literature: (abbreviation in bracket)
1. M. Green, J. Schwarz and E. Witten (GSW), "Superstring theory",
volume I and II
(Cambridge University Press 1987).
2. J. Polchinski (JP), "String theory", volume I and II
(Cambridge University Press 1998).
3. D. Lüst and S. Theisen (LT), "Lectures on string theory",
(346 Lecture Notes in Physics, Springer Verlag 1989).
You can find the book here as Part 2, Part 3.
"Part one",
4. C. V. Johnson, "D-branes" (Cambridge monographs on mathematical physics 2003)
5. K. Becker, M. Becker, and J.H. Schwarz (BBS), "String theory and M-theory",
(Cambridge Univ Press 2007)
Recent books debating the pros and cons of string theory
L. Smolin, "The trouble with physics" (Houghton Mifflin Company, 2006)
P. Woit, "Not even wrong" (Jonathan Cape, 2006)
see also comments on these by J. Polchinski:
Guest Blogger: Joe Polchinski on String Debates
General high-energy physics:
A very nice overview of elementary particle physics, gravitation and cosmology, Kaluza-Klein,
supersymmetry and introductory string theory can be found in
"Particle physics and cosmology", by P.D.B. Collins, A.D. Martin and E.J. Squires (Wiley 1989).
Literature discussing unification and reductionism
"Dreams of a final theory", Stephen Weinberg (Vintage 1992): Very good!!
"The emperor's new mind", Roger Penrose (Penguin 1989)
Some articles from Physics Today and New Scientist:
Witten, Physics Today, April 1996, p. 24-30
Kane, Physics Today, Febr 1997, p. 40-42
Collins, Physics Today, March 1997, p. 19-22
Witten, Physics Today, May 1997, p. 28-33
Kane and Witten, New Scientist, 30 March 2002, p. 28-32
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About the book
The 2009 version of the Master course String/M theory is based on the
new and much improved 2nd edition of the book "A first course in string theory"
by Barton Zwiebach. This book gives an extremely pedagogical introduction to
this rather difficult subject by starting from physics familiar to all undergraduate
students having studied physics for two years at the university. The required knowledge of
mathematics is kept at a minimum by providing detail explanations of all
the mathematics used in the book that is not part of the first year mathematics
curriculum.
All the necessary aspects of field theory, from electromagnetism to gravity,
and quantum mechanics are explained from scratch and developed just to the
level needed for the application in question.
A large number of exercises and problems appear at the end of each chapter
some of which will be used as home exam problems for this course.
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Examination:
Home problems and a successful oral exam for highest mark (CTH: 5, GU: VG)
Limits for different marks: You can get 3 points per problem
GU:
V requires 40% of the total points
VG requires 70% of the total points plus a successful oral exam
CTH:
3 requires 40% of the total points
4 requires 60% of the total points
5 requires 80% of the total points plus a successful oral exam
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NOTE: The links below suggest extra reading material that is not included in the course requirements
and will not appear in the oral exam (unless the article is used in a home exam problem).
NOTE: The exercises in the text book called "Quick calculations" are generally very nice and
give a good check that you have understood the material.
You should try to do them without exception.
NOTE: All home problems are taken from the 2nd edition of the book by Zwiebach!!
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1st WEEK (calender week 11): Introduction and basic aspects from field theory
Lecture 1: Tuesday March 16, at 15.15 Introduction: Chap 1 and 2,
and parts of chap 23 (pages 525-527), in Zwiebach´s book (BZ)
Read also Chap 1 and 2 of the review talk by Horowitz
"Introduction to Holographic Superconductors",
which gives some more info on this very hot current research topic based on AdS/CFT!.
Note that these ideas are related to those presented in Chap 23 i BZ!
Further reading:
String/M theory introduces extra dimensions. Have a look at the history of such
by reading Stanley Deser's account
"The many dimensions of dimension",
and the first few pages in the article
"Perspectives on issues beyond the standard model"
by G. Kane.
Another recent comment about string predictions can be found in the article
"String theory predicts an experimental result"
Further reading:
For a recent discussion of units and fundamental constants in nature, see Mike Duff
"Comment on time variation of fundamental constants ".
and for comments on extra dimensions, you may read
"Why do we live in four dimensions".
and the first three or four pages in F. Ferugio's
review article
"Extra dimension in particle physics".
That the start of LHC is stirring up interest and emotions among the public is clear from
"LHC in US lawsuit".
(An excellent but a bit more advanced account of large extra dimensions and microscopic black holes
can be found in "this article by Kanti".)
Lecture 2: Thursday March 18, at 10.00 Field theories in various dimensions, the Planck length:
Chapter 3 in BZ
Recommended exercises from BZ: 2.1, 2.2, 2.3, 3.1, 3.3, 3.7, and 3.8
Home exam problem 1: Solve problem 23.6 in BZ.
Home exam problem 2: Solve problem 2.7 in BZ.
Dead-line for handing in home exam problems 1 and 2: April 8.
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2nd WEEK (calender week 12): Point particles and strings: the classical story
Lecture 3: Monday March 22 at 15.15 Non-relativistic strings and relativistic point particles: Chapters 4 and 5 in BZ
Lecture 4: Tuesday March 23 at 15.15 The relativistic string: Chapter 6 in BZ
NOTE: No lecture on Thursday this week!
Recommended exercises from BZ (2nd ed): 4.6, 5.3, 5.4, 5.5, 5.6, 6.1, 6.2, .
Home exam problem 3: Solve problem 4.4 in BZ
Home exam problem 4: Solve problem 6.10 in BZ
Dead-line for handing in home exam problems 3 and 4 is April 15.
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Calender week 13: Easter holiday: No lectures!
We start again on Tuesday April 6 at 15.15!
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3rd WEEK (calender week 14): More classical string theory
Lecture 5: Tuesday April 6 at 15.15 String parametrization and world-sheet currents
Read chapters 7 and 8 in BZ (Section 7.6 is not included in the course.).
Note the slope parameter \alpha^{\prime} at the end of chapter 8 in BZ.
Lecture 6: Thursday April 8 at 10.00 The light-cone relativistic string: Read chapters 9 in BZ.
This chapter is one of the central parts of this course and crucial for the understanding of string theory.
To prepare for this lecture try to summarize the three steps in Chap 6 and 7 in which the world sheet
coordinates tau and sigma are chosen and what the results of these choices are.
Recommended exercises: BZ problem 7.1, 8.6, 8.7, 9.1 and 9.2 ,
Home exam problem 5: Solve problem 7.5 in BZ
Home exam problem 6: Solve problem 9.3 in BZ
Dead-line for handing in home exam problems 5 and 6 is April 22
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4th WEEK (calender week 15):
Light cone fields, particles, and strings: the quantum case.
Lecture 7: Monday April 12 at 10.00:NOTE-extra lecture!!!
Last parts of chapter 9: mode expansions and Virasoro generators!
These are basic ingredients in the coming discussions of string theory.
Lecture 8: Tuesday April 13 at 15.15
Field theories of spin zero, one and two: light cone and quantum: Chap 10 in BZ
Important discussion about gauge invariance and application of light cone methods in field theory.
The relativistic quantum point particle (Chapter 11 in BZ)
Read this chapter carefully; many important points are here explained in a
simpler setting than string theory: gauge fixing, compensating transformations,
quantization both in the light cone gauge and covariant (as done later in Chapter 21 for the string).
Lecture 9: Thursday April 15 at 10.00
The relativistic quantum open string (Chapter 12 in BZ)
This chapter contains for the first time in this course material that we normally
refer to as "string theory": quantized string coordinates and Virasoro generators and their
algebra, and the mass spectrum and its interpretation. These last concepts are
vital for understanding the rest of the course.
Recommended exercises: problems 10.3, 10.4, 11.5 and 12.1-12.4in BZ
Home exam problem 7: Solve problem 10.6 in BZ
Home exam problem 8: Solve problem 11.6 in BZ
Dead-line for handing in home exam problems 7 and 8 is April 29
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5th WEEK (calender week 16): The open and closed quantized bosonic strings
NOTE: Extra Lecture this week on Monday
Lecture 10: Monday April 19 at 10.00
Review of the light cone quantization of open bosonic strings , and final parts of Chap 12 in BZ.
Lecture 11: Tuesday April 20 at 15.15
The closed quantized bosonic string, spectrum in trivial and orbifolded target spaces: Chap 13 in BZ
Lecture 12: Tuesday April 22 at 10.00
The quantum superstring: a brief introduction to the string and its field theory.
Have a look at chap. 14, (note that sections 14.6 and 14.7 are not included)
and read the lecture notes (they only partly overlap with chap 14 in the book!).
Recommended exercises: 12.3, 12.4, 12.5, 12.7, 12.8, 13.2, 13.3, 14.1-14.4, 14.7 and 14.8 in BZ problem
Home exam problem 9: Solve problem 12.6 in BZ
Home exam problem 10: Solve problem in 14.3 BZ
Dead-line for handing in home exam problems May 6
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6th WEEK (calender week 17): The superstring and "advanced topics": D-branes
Lecture 13: Tuesday April 27 at 15.15
This lecture gives a brief account of the different superstrings and the role of M-theory,
mostly following Chapter 14 in BZ. The landscape (see below) will be discussed later.
"The string landscape": Recent developments in string/M theory point towards a more
complex connection between the theory and our dynamical universe. This has led to a heated
debate about the role of the anthropic principle in the context of the "landscape".
For an introductory discussion of the "string landscape", see Stephen Weinberg's paper
"Living in the multiverse".
In particular the final paragraph gives a feeling for the "heat" in this debate.
Part II in Zwiebach: Developments
When now we turn to applications in the second part of the book ("Developments") it is of vital
importance to fully master the arguments and results of the chapters 11-13 and have some
understanding of Chapter 14 on the superstring.
Lecture 14: Thursday April 29 at 13.15 NOTE THE TIME!
D-branes, charges and gauge fields: read Chapters 15 and 16 in BZ
Home exam problem 11: Solve problem 16.5
Home exam problem 12: Solve problem 23.5. Then read Chapter 3 in
"Quantum criticality and black holes"
and answer the following AdS/CFT related questions:
1. how is the metric of the AdS4 boundary identified?
2. what are the two roles of the group SO(3,2)?
3. give two forms of the black hole metric in AdS4!
4. show how to take the Minkowski limit to obtain a Schwarzschild black hole metric
from an AdS black hole.
THESE ARE THE LAST HOME PROBLEMS!!
Dead-line for handing in home exam problem is May 11
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7th WEEK (calender week 18): Advanced topics: Dualities
Lecture 15: Tuesday May 4 at 15.15
T-duality in string theory: Chapter 17 in BZ
Lecture 16: Thursday May 6 at 10.00
More on T-dualities: parts of Chapter 18 br>
NOTE: Chapters 19 and 20 are not included in the course!
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8th week (calender weeks 19): Effective field theories on branes, supergravity, duality and M-theory
NOTE: Do not forget to schedule your oral exam!
Monday May 17 and the week May 24 to 28 are possible!
Lecture 17: Tuesday May 11 at 15.15 LAST LECTURE!!
String theory and particle physics: read Chapter 21, sections 1-3,in BZ.
The rest of the chapter is nice reading but will not appear in the examination.
Effective field theories on branes and in the bulk, supergravity and some
AdS/CFT (read the lecture notes and Chapter 23, sections 4 to 8.)
An interesting recent article that tries to give an overview of high energy physics at the level of
this course
"Developments in high energy theory".
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BELOW IS THE COURSE FROM LAST YEAR!!!!!!!
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9th week(calender weeks 22): Examination week
Examination:Please schedule the oral exam with me a soon as possible.
The last day possible for the oral exam is Thursday May 28.
NOTE: Limits for different marks: You can get 3 points per problem
GU:
V requires 40% of the total points
VG requires 70% of the total points plus a successful oral exam
CTH:
3 requires 40% of the total points
4 requires 60% of the total points
5 requires 80% of the total points plus a successful oral exam
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