String/M theory, MSc course, 7.5 p, Lp IV 2009
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Course codes: CTH: FFM 485 and GU: FY 4850
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Introductory meeting 2009: Tuesday, March 17, 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 12): chapters 1-3
week 2 (calender week 13): chapters 4-6
week 3 (calender week 14): chapters 7-10
week 4 (calender week 17): chapters 11-12
week 5 (calender week 18): chapters 13-14, parts of 24
week 6 (calender week 19): parts of chapters 15-17
week 7 (calender week 20): parts of chapters 18-21
week 8 (1/2 calender week 21): parts of chapter 23
week 9 (calender week 22): examination
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NEW Schedule: All lectures in Origo 6115
There will in general be three 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
Fridays at 08.00-09.45
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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:
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 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 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 12): Introduction and basic aspects from field theory
Lecture 1: Tuesday March 17, at 15.15 Introduction: Chap 1 in Zwiebach´s book (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"
Lecture 2: Wednesday March 18, 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, 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 3: Thursday March 19, 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 2.5 in BZ. (=2.4 in 1st edition)
Home exam problem 2: Solve problem 2.7 in BZ. (not in 1st edition)
Home exam problem 3: Solve problem 3.10 in BZ. (=3.9 in 1st edition)
Dead-line for handing in home exam problems 1-3 is March 31.
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2nd WEEK (calender week 13): Point particles and strings: the classical story
Lecture 4: Monday March 23 at 15.15 Non-relativistic strings and Lagrangian formulations: Chapter 4 in BZ
Lecture 5: Tuesday March 24 at 15.15 The relativistic point particle: Chapter 5 in BZ
Lecture 6: Thursday March 26 at 10.00 The relativistic string: Chapter 6 in BZ
Recommended exercises from BZ (2nd ed): 4.6, 5.3, 5.4, 5.5, 6.1, 6.2, .
Home exam problem 4: Solve problem 4.4 in BZ (=4.3 in the 1st edition)
Home exam problem 5: Solve problem 5.6 in BZ (in both editions)
Home exam problem 6: Solve problem 6.7 in BZ (=6.4 in the 1st edition)
Dead-line for handing in home exam problems 4, 5 and 6 is April 21.
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3rd WEEK (calender week 14): More classical string theory
Lecture 7: Monday March 30 at 15.15 Classical string motion: Chapter 7 in BZ.
Lecture 8: Tuesday March 31 at 15.15
World-sheet currents and the slope parameter \alpha^{\prime}: Chapter 8 in BZ.
Lecture 9: Friday April 3 at 08.00 The light-cone relativistic string and field theory: Chapters 9 in BZ.
Recommended exercises: BZ problem 7.1, 7.5, 8.6, 8.7, 9.1 and 9.2 ,
Home exam problem 7: Solve problem 7.3 in BZ (in both editions)
Home exam problem 8: Solve problem 8.5 in BZ (8.3 in first edition)
Home exam problem 9: Solve problem 9.3 in BZ (in both editions)
Dead-line for handing in home exam problems 7 to 9 is May 5
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4th WEEK (calender week 17):
Light cone fields, particles, and strings: the quantum case.
Lecture 10: Monday April 20 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.
Lecture 11: Tuesday April 21 at 15.15
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 12: Thursday April 23 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 and 11.5 in BZ
Home exam problem 10: Solve problem 10.6 in BZ (in both editions)
Home exam problem 11: Solve problem 11.6 in BZ (in both editions)
Dead-line for handing in home exam problems 10 and 11 is May 12
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5th WEEK (calender week 18): The open and closed quantized bosonic string
NOTE: Lectures this week only on Monday and Tuesday at 13.15. Thursday off!
Lecture 13: Monday April 27 at 15.15
Review of the light cone quantization of open bosonic strings , and final parts of Chap 12 in BZ.
Lecture 14: Tuesday April 28 at 15.15
The closed quantized bosonic string, spectrum in trivial and orbifolded targetspaces: Chap 13 in BZ
Recommended exercises: 12.3, 12.4, 12.5, 12.7, 12.8, 13.2 and 13.3 BZ problem
Home exam problem 12: Solve problem 12.12 in BZ (=12.10 in first edition)
Home exam problem 13: Solve problem 13.5 in BZ (same in first edition)
Dead-line for handing in home exam problems 12 and 13 is May 18
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6th WEEK (calender week 19): The superstring and "advanced topics": D-branes
Lecture 15: Monday May 4 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 16: Tuesday May 5 at 15.15
D-branes and gauge fields: Chap 15 in BZ
Lecture 17: Thursday May 7 at 10.00
String charge and electric charge: Chap 16 in BZ
Recommended exercises:
Home exam problem 14: Solve problem 14.3 in BZ (13.7 in 1st ed)
Dead-line for handing in home exam problem is May 18
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7th WEEK (calender week 20): Advanced topics: Dualities
NOTE: The lecture on Thursday postponed till Tuesday next week!
Lecture 18: Monday May 11 at 15.15
T-duality in string theory: Chaps 17 in BZ
Lecture 19: Tuesday May 12 at 15.15
More on T-dualities: parts of Chaps 18, 19 and 20 in BZ
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8th week (calender weeks 21): Effective field theories on branes, supergravity, duality and M-theory
NOTE: Don´t forget to schedule your oral exam!
The last day possible for the oral exam is Thursday May 28.
Lecture 20: Monday May 18 at 15.15
String theory and particle physics: Chap 21 in BZ.
Lecture 21: Tuesday May 19 ar 15.15
Effective field theories on branes and in the bulk, supergravity; overview (lecture notes only)
Summary and introduction to M-theory (lecture notes only)
An interesting recent article that tries to give an overview of high energy physics at the level of
this and other Fundamental physics master courses is
"Developments in high energy theory".
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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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