Advanced String/M theory, Graduate course, 5p, Lp I-II Fall 2007
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Course codes: CTH: -- and GU: --
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Introductory meeting 2007: Wedenesday, 5 September at 10.00 in Origo 6115
(the physics building called Origo, 6th floor, north wing).
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Schedule: All lectures in Origo 6115
Wednesdays at 10.00-12.00
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Teacher: Professor Bengt E.W. Nilsson, phone 772 3160, Origo 6104C
Course assistant: Christoffer Petersson, phone 772 3183, Origo 6111
Literature:
"String theory in a nutshell", Elias Kiritsis,
(Princeton university press, 2007).
Note that the lectures will not follow this book chapter by chapter, and some material
not discussed in the book will be covered.
Additional literature:
1. "A first course in string theory", Barton Zwiebach
(Cambridge university press, 2004).
2. "String theory and M-theory, a modern introduction", Katrin Becker, Melanie Becker and
John H. Schwarz (Cambridge university press, 2007).
Additional reading:
Recent popular articles:
Article by M. Chalmers in Physics World (very good and up to date)
Stringscape
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)
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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Examination:
Home problems mostly from the book by Kiritsis.
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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Lecture 1: Wednesday, September 5, at 10.00: Introduction to classical branes
Nambu-Goto and Polyakov actions for p+1-dimensional surfaces, so called p-branes.
Further reading:
"The many dimensions of dimension",
by Stanley Deser, and the first few pages in the article
"Perspectives on issues beyond the standard model"
by G. Kane,
and for articles debating what string theory is, see
Ulf Danielsson in Fysikaktuellt nr 2, May 2007, and
the lecture by David Gross at Strings 2007.
Recommended exercises: Problems 2.8, 2.9, and 2.11 in Kiritsis.
Home exam problem 1: Problem 2.7 in Kiritsis.
Lecture 2: Wednesday, September 12, at 10.00: Classical string theory
Symmetries, conserved currents and the stress tensor
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".
Recommended exercises: Problems 2.12, 2.15, and 2.17 in Kiritsis.
Home exam problem 2: Problem 2.14 in Kiritsis.
Lecture 3: Wednesday, September 19, at 10.00: The quantized bosonic string
Mode expansions, quantization, Wick rotation, the X(z,\bar{z}) two-point function,
vertex operators, normal ordering, OPE, the Virasoro algebra.
Recommended exercises: Problems 4.1, 4.2, and 4.9 in Kiritsis.
Home exam problem 3: Problem 4.10 in Kiritsis.
Lecture 4: Wednesday, September 26, at 10.00: Representations of the Virasoro algebra and physical states
More on the Virasoro algebra, vertex operators, representations, modules and unitary c>1 models.
Minimal models and operator algebra.
Recommended exercises: Problems 4.11, 4.13, and 4.16 in Kiritsis.
Home exam problem 4: Problem 4.15 in Kiritsis.
Lecture 5: Wednesday, October 3, at 9.00: Scattering amplitudes and their symmetries
Summary of possible extensions of the Virasoro algebra. Scattering amplitudes and their symmetry properties
The 2d sphere and some string related facts.
Recommended exercises: Problems 4.4, 4.5 and 4.10 in Kiritsis.
Home exam problem 5: Problem 4.6 in Kiritsis.
Lecture 6: Wednesday, October 10, at 9.00: Scattering amplitudes and the origin of ghosts
Ward identities. Final form of scattering is derived and arguments for the use of ghosts presented.
Recommended exercises: Problems 4.27, 5.2 and 5.4 in Kiritsis.
Home exam problem 6: Problem 4.28 in Kiritsis.
Lecture 7: Wednesday, October 17, at 9.00: Loop amplitudes in the bosonic string
The 1-loop amplitude. Modular invariance. Theta functions and other torus related functions.
Recommended exercises: Problems 5.3 and 5.5 in Kiritsis.
Home exam problem 7: Problem 5.6 in Kiritsis.
Lecture 8: Wednesday, October 24, at 9.00: Modular forms and theta functions
Cont. from previous lecture: Partition functions and the modular group.
Recommended exercises: Problems - in Kiritsis.
Home exam problem 8: Problem 5.10 in Kiritsis.
Lecture 9: Wednesday, October 31, at 9.00: Cont. from prev. lecture
More on modular functions and theta functions.
Home exam problem 9: See next week!
Lecture 10: Wednesday, November 7, at 9.00: The string path integral and origin of ghosts
The path integral is defined and analyzed in detail.
Home exam problem 9 and 10: Problem 3.12 and 3.13 in Kiritsis
Lecture 11: Monday, November 12, at 13.15: Cont.: The string path integral and origin of ghosts
The path integral is expressed in terms of ghosts and their role explained.
Home exam problem 11: Derive the stress tensor for the j=2 b,c system first in a real index basis
and then in complex indices.
Lecture 12: Wednesday, November 21, at 8.30: Beta functions and effective field theory
More on ghosts. The path integral in generalbackgrounds and beta-functions.
Lecture 13: Wednesday, November 28, at 8.30: Cont. of Beta functions and effective field theory
Lecture 14: Wednesday, December 5, at 8.30: Torus compactification and Kac-Moody symmetries
Lecture 15: Wednesday, December 12, at 8.30: Cont. of Torus compactification and Kac-Moody symmetries
Lecture 16: Wednesday, December 19, at 8.30: Superstrings and heterotic strings
This concludes the course: 5 old university credit points are awarded when passed.
The requirements for passing are a follow-up discussion with the lecturer and a minimum of 40 per cent
solved home problems.
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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