Course syllabus
Course-PM
FFM485 / FIM480 String theory lp2 HT19 (7.5 hp)
Course is offered by the department of Physics
Contact details
- examiner: Bengt E.W. Nilsson, tfebn@chalmers.se, office Origo N6.109B, phone 0704-101283
- lecturer: Bengt E.W. Nilsson
- teachers -
- supervisors -
Course purpose
The purpose of the course is to give the student insights into the following features of string/M-theory:
1) the geometric definition of the theory,
2) in what sense it corrects Einstein's theory of gravity, i.e., general relativity,
3) how it can give rise to the physics of the Standard Model of elementary particles,
4) some aspects of the very rich mathematical toolbox,
5) the so called AdS/CFT correspondence (briefly),
6) its predictability: swampland conjectures and de Sitter issues (very briefly).
Schedule
Course literature
"A first course in string theory", Barton Zwiebach (Cambridge, 2004, 2nd Ed. 2009).
This (mandatory) textbook contains a lot of detailed arguments and calculations. It is in most parts quite pedagogical and easy to read but does nevertheless manage to introduce the reader to some rather advanced aspects of string theory. It also contains, in Part 1, a lot of basic background material that most students should already be familiar with from previous courses.
Some more advanced books on string theory are (if you are interested in looking at any of the books below please consult the lecturer first):
1. "Basic concepts in string theory", Ralph Blumenhagen, Dieter Lust and Stefan Theisen (Springer, 2012).
This book is more advanced than Zwiebach and uses more modern mathematical techniques. However, it is quite readable and might be used as a follow-up to the book by Zwiebach.
2. "String theory in a nutshell", E. Kiritsis (Princeton, 2007).
Contains a lot of rather advanced modern material and is very condensed.
3. "Superstring theory, Volumes 1 and 2", M. Green, J. Schwarz, and E. Witten, (Cambridge, 1987).
Fantastic old classic! Good source for detailed advanced calculations but no modern CFT and nothing on dualities, AdS/CFT and M-theory.
First volume contains loop calculations and the second volume includes modern mathematical aspects of for instance Yang-Mills gauge theory.
4. "String theory and M-theory", K. Becker, M. Becker and J. Schwarz (Cambridge 2007).
This book covers many of the more important aspects of string theory that are discussed and used in current research. The presentation is sometimes sketchy but a number of very useful arguments are introduced and explained. This book brings the reader quite far towards the research frontier in a limited number of pages.
5. "Supergravity", D. Freedman and A. Van Proeyen (Cambridge 2012).
This extensive book on supergravity contains most of what there is to know about four-dimensional supergravity with one or two supersymmetries.
6. "Gauge/gravity duality", M. Ammon and J. Erdmenger (Cambridge 2015).
This book provides a thorough introduction into the rich area of AdS/CFT and its applications in particular the connection between string theory/supergravity and condensed matter theories.
Lecture notes in string/M-theory:
A number of people in the field have written up and published lecture notes on the arXiv. One of the more pedagogical ones is
David Tong , DAMPT, Univ of Cambridge, UK, "String theory", arXiv:0908.0333 [hep-th]
These lectures are a bit more advanced than the book by Zwiebach but are quite easy to read. However, they do not contain all necessary mathematical steps to derive the results presented. Instead there is a huge number of nice discussions of concepts and ideas special to string theory. Highly recommended as a next step after the book by Zwiebach.
As a next step in the study of string theory, a more advanced CFT treatment of bosonic string theory can be found in:
"The closed bosonic string", Bengt E.W. Nilsson, condensed hand-written lecture notes in Swedish (Chalmers 1995).
Course design
Chapters and problems refer to the textbook by Zwiebach.
The course covers in 16 lectures (2x45 mins) about 3/4 of the 670 pages (all of Chaps 1 - 14 and parts of Chaps 15 - 21, 23 and 24). No exercise classes are included so the students are expected to learn the mathematical tools from the lectures and by working out the home problems (including the mini-project) that are part of the examination. The huge number of pages covered in the book means that the student should make an effort to extract the more important aspects of the material for instance by writing his/her own summary. The lectures and home problems will of course be most helpful in putting together such a summary, which may also be useful when studying for the oral exam. The so called "Quick calculations" should provide a good check on your understanding when reading the text and are all highly recommended.
Calendar weeks 45-51 (2019) and 3 (2020) in brackets:
Zwiebach Part I: home problems 1 - 14
Week 1 (45): Chapters 1-4
Week 2 (46): Chapters 5-8
Week 3 (47): Chapters 9-12
Week 4 (48): Chapters 13 and 14
Zwiebach Part II: elective project problems 1 - 9
Week 5 (49): Parts of Chapters 15 - 18
Week 6 (50): Parts of Chapters 19 - 21
Week 7 (51): Parts of Chapters 23 and 24
Week 8 (3): Examination (oral and project presentations, both mandatory)
--------------------------------------------------------------------------------------------------------------
Detailed time plan: Lectures and home problems
Zwiebach Part I
------------------------------------------------------------------------------------------------------------------------------------------------
Week 1 (45): Chapters 1-4
Introduction to string theory: unification, reductionism and quantum gravity. Light cone coordinates, orbifolds and extra dimensions. The non-relativistic string.
Chapter 1: Introduction
Hand-in problem 1:
Read Chapters 1 and 2 in the article by M. Duff on extra dimensions (http://arxiv.org/pdf/hep-th/9410046.pdf) and answer the following questions (no computations are needed)
a) what is the main difference between the ideas of Kaluza and those of Klein?
b) how does one arrive at the relation between the Newton constants in 4 and 5 dimensions (first line after eq 8)?
c) what are the changes needed in the ansatz (eq 2) for the 5-dimensional metric to contain 4-dimensional fields with canonical dimensions in eq 8? (Metrics in all dimensions are dimensionless while vector and scalar fileds in four dimensions have dimension M=1/L (in natural units).
d) what is the origin of the U(1) gauge symmetry in the Maxwell sector?
e) how does this Kaluza-Klein theory explain the quantization of the electric charge?
Recommended extra reading:
1. The article by Witten in Physics Today April 1996.
2. The introductory address by David Gross at the 2011 Solvay conference which gives the (almost) current view on string theory including successes and problematic issues.
3. M. Duff on fundamental constants http://arxiv.org/pdf/hep-th/0208093.pdf. The appendix contains an interesting debate between researchers of different opinion on this issue.
4. Hoyle et al on submillimeter tests of gravity (http://arxiv.org/pdf/hep-ph/0011014.pdf). (4 pages).
5. A nice discussion about the crucial idea of unification/reductionism may be found in the book "Dreams of a final theory" by Steven Weinberg (1993).
Chapter 2: Special relativity and extra dimensions, compact manifolds and orbifolds.
Hand-in problem 2: Problem 2.7.
Recommended home problems: 2.1, 2.2, 2.3, 2.4, 2.5*, 2.6 and 2.11.
Chapter 3: EM and gravity in various dimensions. Hand-in problem 3: Problem 3.11.
Recommended home problems: 3.1*, 3.2, 3.3, 3.4, 3.7* and 3.8
Chapter 4: Non-relativistic strings. Hand-in problem 4: Problem 4.5.
Recommended home problems: 4.1, 4.4* and 4.6.
------------------------------------------------------------------------------------------------------------------------------------------------
Week 2 (46): Chapters 5-8.
Relativistic theories for point particles and strings. The static gauge.
Chapter 5: The relativistic point particle. Hand-in problem 5: Problem 5.6.
Recommended home problems: 5.1, 5.2*, 5.3 and 5.7.
Chapter 6: Relativistic strings. Hand-in problem 6}: Problem 6.7.
Recommended home problems: 6.1, 6.2* and 6.6.
Chapter 7: String parametrization and classical motion. Hand-in problem 7: Problem 7.5.
Recommended home problems: 7.1, 7.2 and 7.4*.
Chapter 8: World-sheet currents. Hand-in problem 8: Problem 8.7.
Recommended home problems: 8.1, 8.5* and 8.6.
------------------------------------------------------------------------------------------------------------------------------------------------
Week 3 (47): Chapters 9-12
Light-cone strings and fields. Quantization of point particles and open strings.
Chapter 9: Light-cone relativistic strings. Hand-in problem 9: Problem 9.5.
Important: The covariant constraint formulation. The light-cone solution and mode expansion.
Recommended home problems: 9.1, 9.2 and 9.3*.
Chapter 10: Light-cone fields and particles. Hand-in problem 10: Problem 10.6.
Sections 10.1-10.4 should be familiar at least for those of you who have QFT.
Sections 10.5 and 10.6 contain new material which is very important for the rest of the course.
Recommended home problems: 10.2, 10.3* and 10.4.
Chapter 11: The relativistic quantum point particle. Hand-in problem 11: Problem 11.6.
This chapter is the start of the more intricate aspects of string theory, here examplified by point particles. The light-cone quantization and implementation of Lorentz invariance in the light-cone gauge are a bit tricky but absolutely crucial features that must be understood in detail.
Recommended home problems: 11.1, 11.2 and 11.5*.
Chapter 12: Relativistic quantum open strings. Hand-in problem 12: Problem 12.6.
This is one of the key chapters in the course!
Recommended home problems: 12.1, 12.2, 12.3*, 12.4 and 12.7
------------------------------------------------------------------------------------------------------------------------------------------------
Week 4 (48): Chapters 13 and 14
The closed bosonic and supersymmetric strings in light cone gauge. There is also a covariant version of this that will be discussed later.
If time permits we will present some low energy field theories, i.e., supergravity, and an intro to M-theory.
Chapter 13: The relativistic quantum closed string. Hand-in problem 13: Problem 13.5.
Recommended home problems: 13.1* and 13.2.
Chapter 14: Superstrings and M-theory. Hand-in problem 14: Problem 14.3.
Recommended home problems: 14.1, 14.2 and 14.4*.
------------------------------------------------------------------------------------------------------------------------------------------------
Detailed time plan: Lectures and elective problems for the mini-project
Zwiebach Part II
------------------------------------------------------------------------------------------------------------------------------------------------
Week 5 (49): Parts of Chapters 15 - 18
Elective project problems 1 - 4: will be decided during the course.
Detailed reading instructions: will be decided during the course.
------------------------------------------------------------------------------------------------------------------------------------------------
Week 6 (50): Parts of chapters 19 - 21
Elective project problems 5 - 7: will be decided during the course.
Detailed reading instructions: will be decided during the course.
Recommended extra reading: A very nice review on dualities in field and string theory is the one by Polchinski (http://arxiv.org/pdf/1412.5704.pdf).
------------------------------------------------------------------------------------------------------------------------------------------------
Week 7 (51): Chapters 23 and 24
Parts of Chapter 23: AdS/CFT.
Elective project problem 8: will be decided during the course.
Detailed reading instructions: will be decided during the course.
Recommended extra reading: Reviews slightly above the level of Chapter 23:
1. Hartnoll, (http://arxiv.org/pdf/0903.3246.pdf)
2. Lucini and Panera, chapters 1 and 2 (http://arxiv.org/pdf/1309.3638v1.pdf)
3. Ramallo chapters 1-7 (http://arxiv.org/pdf/1310.4319v3.pdf)
4. M. Natsuume, "AdS/CFT Duality User Guide", (http://arxiv.org/pdf/1409.3575.pdf)
Parts of Chapter 24: Covariant quantum string theory.
Elective project problem 9: Problem 24.2.
Detailed reading instructions: will be decided during the course.
------------------------------------------------------------------------------------------------------------------------------------------------
Week 8 (2): Time for studies
------------------------------------------------------------------------------------------------------------------------------------------------
Week 9 (3): The mandatory oral exam and project presentation.
Book a time for your oral exam by sending the lecturer an email with a suggested time.
Changes made since the last occasion
--
Learning objectives and syllabus
Learning objectives:
After having passed the course 'String theory' the student should have acquired some understanding of the basic clash between General Relativity and Quantum Mechanics, and how this clash is resolved in string theory. The student should also have obtained a set of mathematical tools making it possible to compute various physical effects in string theory, and knowledge of how the gravitational force and the standard model of elementary particles are extracted from string theory and its so called D-branes. He/she should also be able to quantize the string and express it in terms of the infinite dimensional Virasoro algebra. Also very important is the expected ability to discuss and evaluate the good and weak points of string theory and its relation to physics in four-dimensional spacetime. Finally, the student should also have acquired some understanding of the AdS/CFT correspondence and how it can be applied to, e.g., condensed matter physics.
Link to the syllabus on Studieportalen.
Chalmers: Study plan (also for GU)
Examination form
Home problems, a small project (report and presentation) and a mandatory (45 minutes) oral exam at the end.
The final grade is obtained using the following weights:
Home problems: 30 % (one from each of the 14 chapters of part I of the book)
Project: 10 % (one selected problem from part II of the book)
Oral exam: 60%
The 14 home problems are to be handed in and will give up to 3 points each. To be eligible for the oral exam half of the points must be obtained. The purpose of the home problems and the project is to get some familiarity with the mathematical methods of string theory while the oral will test the general understanding of string theory, in particular the concepts that a special to the theory. The oral will also check that the student has correctly understood the things studied in the home problems and the various projects.
Course summary:
| Date | Details | Due |
|---|---|---|