String/M theory, Master course, 5p, Lp IV 2006
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Course codes: CTH: FFM 485 and GU: FY 4850
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Introductory meeting 2006: Wednesday 15 March at 13.00 in Origo FL63
(the physics building called Origo, 6th floor).
Teacher: Professor Bengt E.W. Nilsson, phone 772 3160, Origo 6104C
Literature: "A first course in string theory", Barton Zwiebach,
(Cambridge university press 2004).
Available at Cremona and on the net for <600 SEK.
Tentative study plan for the course:
week 1 (calender week 11): chaps 1-3
week 2 (calender week 12): chaps 4-6
week 3 (calender week 13): chaps 7-10
week 4 (calender week 14, Monday only at 09.30): chaps 11-13
week 5 (calender week 17): chap 21 and lecture notes on superstrings
week 6 (calender week 18): parts of chaps 14-16
week 7 (calender week 19): parts of chaps 17-20
week 8 (calender week 20): examination
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Schedule: Monday, Wednesday, and Friday at 10.00 in Origo 6115.
Examination:
Home problems and a successful oral exam for highest mark (CTH: 5, GU: VG)
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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 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)
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:
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
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About the book
The 2006 version of the Master course String/M theory is based on the
new 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 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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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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WEEKLY SCHEDULE Lp IV 2006
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NOTE: The links below suggest extra reading material that is not included in the course requirments
and will not appear in the oral exam (unless the article is used in a home exam problem).
NOTE: The exercises in the text 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.
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1st WEEK (calender week 11): Introduction and basic aspects from field theory
Lecture 1: Wednesday March 15, at 15.15 Introduction (Chapter 1 in B.
Zwiebach's (BZ) book)
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.
Lecture 2: Friday March 17 at 10.00 Units, special relativity and extra dimensions
(Chapter 2 in BZ)
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, read the first three or four pages in F. Ferugio's
review article
"Extra dimension in particle physics".
Lecture 3: Friday March 17 Field theories in various dimensions, the Planck length
(Chapter 3 in BZ)
Recommended exercises from BZ: 2.2, 2.3, 3.3, 3.4 and 3.7
Home exam problem 1: Solve problem 2.1 in BZ.. Read the article by M. Duff (see link
from lecture 2)
and explain the difference between fundamental dimensionful constants like c, and coupling
constants like e .
NOTE: Only problem 2.1 needs to be handed in , but questions on the article by Duff may
occur in the oral exam.
Home exam problem 2: Solve problem 2.4 in BZ.
Home exam problem 3: Solve problem 3.9 in BZ.
Dead-line for handing in home exam problems 1-3 is March 24.
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2nd WEEK (calender week 12): Point particles and strings: the classical story
Lecture 4: (Ling Bao) Non-relativistic strings and Lagrangian formulations (Chapter 4 in BZ)
Lecture 5: (Ling Bao) The relativistic point particle (Chapter 5 in BZ)
Lecture 6: The relativistic string (Chapter 6 in BZ)
Recommended exercises: BZ problems 4.6, 5.1, 5.2, 5.4, 5.5, and 5.7 if you have taken GR.
Home exam problem 4: Solve problem 4.3 in BZ
Home exam problem 5: Solve problem 5.6 in BZ
Home exam problem 6: Solve problem 6.6 in BZ
Dead-line for handing in home exam problems 4, 5 and 6 is March 31.
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3rd WEEK (calender week 13): More classical string theory
Lecture 7: Classical string motion (Chapter 7 in BZ).
Advanced track 1 on an alternative action, the "Polyakov action".
Lecture 8: World-sheet currents and the slope parameter \alpha^{\prime} (Chapter 8 in BZ)
Lecture 9: The light-cone relativistic string and field theory (Chapter 9 and 10 in BZ)
Recommended exercises: BZ problems 7.2, 8.2, 8.4, 9.1, 9.3, 10.2 and 10.3,
Home exam problem 7: Solve problem 7.5 in BZ
Home exam problem 8: Solve problem 8.3 in BZ
Home exam problem 9: Solve problem 9.2 in BZ
Home exam problem 10: Solve problem 10.6 in BZ
Dead-line for handing in home exam problems 7 to 10 is April 28
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4th WEEK, lecture only on Monday(calender week 14):
Light cone particles, strings and superstrings: classical and quantum,
Lecture 10-11: Monday 09.30-12.00
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 covariant and in the light cone gauge (as done later for the string).
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.
The relativistic closed string (Chapter 13 in BZ)
Read the bosonic closed string material carefully and have a look at the last section
on the superstring. We will start week 5 by summarizing the material in chaps 11-13 and
then spend the rest of that week discussing covariant string theory (chap 21) and superstring
theory (lecture notes).
When 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 in BZ.
"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.
Recommended exercises: BZ problem 11.4, 11.5, 12.2 and 12.7
Home exam problem 11: Solve problem 11.6 in BZ
Home exam problem 12: Solve problem 12.3 in BZ
Home exam problem 13: Solve problem 12.10 in BZ
Home exam problem 14: Solve problem 13.5 in BZ
Dead-line for handing in home exam problems 10 to 14 is May 5
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5th WEEK (calender week 17): Covariant aspects of quantized strings and superstrings
NOTE: Lectures this week: Monday and Friday at 15.15-17.00, Wednesday at 13.15.
Lecture 12:
Review of the light cone quantization of open and closed bosonic strings (chaps 12 and 13).
Covariant quantization of the bosonic string (Chapter 21)
Lecture 13: Cont. with chap 21. Intro to quantized superstrings
(Read lecture notes and section 13.5 in BZ)
Lecture 14: More on superstrings, some effective field theory, and the
role of M-theory (lecture notes only)
Recommended exercises: BZ problem 21.3 and 21.5
Home exam problem 15: Solve problem 21.2 in BZ
Home exam problem 16: Solve problem 13.7 in BZ
Dead-line for handing in home exam problems 15 and 16 is May 5
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6th WEEK (calender week 18): Advanced topics: D-branes
Lecture 15: at 10.00 Wednesday May 3
More on superstrings, cont. from last week: lecture notes
Lecture 16: at 10.00 Friday May 5
D-branes: parts of Chapter 14 and 15 in BZ
Recommended exercises: 14.1 and 15.3
Home exam problem 17: Solve problem 14.6 in BZ
Home exam problem 18: Solve problem 15.7 in BZ
Dead-line for handing in home exam problems 17 and 18 is May 12
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7th WEEK (calender week 19): Advanced topics: Dualities
Lecture 17: at 10.00 Monday May 8
D-branes: Parts of Chaps 14 in BZ
Lecture 18: at 10.00 Wednesday May 10
String charge: Parts of Chap 15 in BZ
Lecture 19: at 10.00 Friday May 12
T-duality in string theory: Chaps 17 and 18
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8th and 9th WEEKS (calender weeks 20-21): Final lecture om Monday and examination
Lecture 20: at 10.00 Monday May 15
Effective field theories on branes and in the bulk; overview
Examination:Please schecule the oral exam with me a soon as possible.
The last day possible for the oral exam is May 24.
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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