Course syllabus

Course-PM

String theory (FFM485 / FIM480), lp 2, HT 2020 (7.5 hp)

The course is offered by the Department of Physics

The course will be given as 16 lectures on zoom. An email invitation to zoom will be sent to you a few minutes before the start of each lecture: Use the link to participate in the lecture.

Lecture notes are provided in one single big pdf-file (see link below or "Files") which defines the course together with the textbook by Barton Zwiebach (BZ) (see below) and the home problems. The pdf-file will be updated continuously during the course so please make sure you are using the latest version. The same applies to this syllabus!

Instructions on what to read in BZ, including which home problems to solve (as part of the examination), are given below for each chapter of the book. Some extra material is included in the course and appears only in the lecture notes (i.e., not in BZ). You will also find links to other texts below, both popular and research papers, that you are highly recommended to look at. These will, however, not be discussed in the oral exam unless it is specifically said that they are part of the course.

For more information on the examination process see the end of the syllabus.

Please don't hesitate to contact the lecturer via email if you have any kind of questions on the lectures or the home problems. Also general comments on the course are most welcome.

Contact details

examiner: Bengt E.W. Nilsson, tfebn@chalmers.se, phone 0704-101283
lecturer: Bengt E.W. Nilsson
teachers -
supervisors -
Course representatives: Alex Bökmark, Kirill Danilov, Joel Karlsson, Eric Nilsson and Ludvig Svensson.

Course purpose

The purpose of the course is to give some insights into the following features of string/M-theory;

1) the geometric definition of the theory,

2) the role of extra dimensions beyond our usual ones, time and three space,

3) in what sense it corrects Einstein's theory of gravity, i.e., general relativity,

4) how it can give rise to the physics of the Standard Model of elementary particles,

5) some aspects of the very rich mathematical toolbox,

6) the so called AdS/CFT correspondence (briefly),

7) its predictability: swampland conjectures and de Sitter issues (very briefly).

Schedule

TimeEdit

Course literature

"A first course in string theory", Barton Zwiebach (BZ) (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. "Superstring theory, Volumes 1 and 2", M. Green, J. Schwarz, and E. Witten, (Cambridge, 1987).

Fantastic old classic! It is a very good source for detailed advanced calculations but has nothing on modern CFT, dualities, AdS/CFT and M-theory.

First volume contains loop calculations and the second volume includes some modern mathematical aspects of Yang-Mills gauge theory.

3. "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 concepts and arguments are introduced and explained. This book brings the reader quite far towards the research frontier in a limited number of pages.

4. "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.

5. "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

"String theory", by David Tong , DAMPT, Univ of Cambridge, UK, 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 the mathematical steps necessary to derive the results. Instead there is a huge number of nice discussions of concepts and ideas special to string theory. It is highly recommended as a next step after the book by Zwiebach.

A more advanced CFT treatment of the bosonic string theory can be found in:

"The closed bosonic string", Bengt E.W. Nilsson, condensed hand-written lecture notes in Swedish (Chalmers 1995). It contains loop calculations and modern CFT techniques, as well as an introduction to some more advanced string mathematics.

Compactifications are discussed in detail in the review:

"Kaluza-Klein supergravity", M.J. Duff, B.E.W. Nilsson and C.N. Pope, Physics Reports Vol 130, pages 1 - 142 (1996).

Course design

Chapters and problems refer to the textbook by Barton Zwiebach (BZ).

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). There are no exercise classes 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 define the course and 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" in the BZ textbook should provide a good check on your understanding when reading the text and are all highly recommended.

Brief course plan: Calendar weeks 45 - 51 (2020) and 2 - 3 (2021) in brackets:

BZ Part I: Chapters 1 - 14 plus 24. Home problems 1 - 14

Week 1 (45): Chapters 1-4 (2 lectures)

Week 2 (46): Chapters 5-10 (3 lectures)

Week 3 (47): Chapters 11-12 (2 lectures)

Week 4 (48): Chapters 13 and 24 plus extra material (3 lectures)

Week 5 (49): Chapter 14 plus extra material (2 lectures)

BZ Part II: Chaps 15 - 21 and 23. One small project with a written report and presentation (on zoom)

Week 6 (50): Parts of Chapters 15 - 20 briefly (2 lectures)

Week 7 (51): Parts of Chapters 21 and 23 briefly plus outlook (2 lectures)

Week 8 (2): Possibly an extra zoom session: Questions etc. (The project presentation session?)

Week 9 (3): Examination (oral and project presentations, both mandatory)

Detailed time plan: Lectures, home problems and reading instructions

Lecture notes:

Zoom-lectures-2020.pdf

Barton Zwiebach Part I

Week 1 (45), 2 lectures: Chapters 1-4

Introduction to string theory: unification, reductionism and quantum gravity. Light cone coordinates, orbifolds and extra dimensions. The non-relativistic string.

Recommended extra reading:

1. The article by Witten in Physics Today April 1996.

Witten-1996-Physics Today.pdf

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.

Gross at Solvay 2011.pdf

3. Mike Duff's paper on the time and space independence of fundamental constants http://arxiv.org/pdf/hep-th/0208093.pdf. The appendix contains an interesting debate between researchers with different opinions on this issue.

4. 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 1: Introduction

Reading instructions: Read Chap 1 in BZ and the lecture notes which emphasise the important points.

Home problem 1: See lecture 1 in the pdf-file Lecture notes. Deadline: Noon Nov. 13, 2020. This home problem concerns issues discussed in sections 1 and 2 of Mike Duff's paper

Duff-on extra dimensions-9410046.pdf

Chapter 2: Light-cone coordinates, extra dimensions, compact manifolds and orbifolds.

Reading instructions: Sections 2.3 - 2.10 are rather short but each one contains an issue that is very important for the rest of the course.

Read the first of the four pages of the paper by Hoyle et al on submillimeter tests of gravity (http://arxiv.org/pdf/hep-ph/0011014.pdf) as part of the course:

Hoyle-submilimeter tests - 0011014.pdf

Recommended problems: 2.1, 2.2, 2.3, 2.4, 2.5*, 2.6 and 2.11.

Home problem 2: Do BZ problem 2.7. Deadline: Noon Nov. 13, 2020.

Chapter 3: EM and gravity in various dimensions.

Reading instructions: Basically only familiar material up until the important eq. 3.74 in sect. 3.5. Sections 3.6 - 3.10 contain the gravity side of the story and are all important (but a summary will be rather short). See lecture notes for some alternative arguments.

Home problem 3: Do BZ problem 3.11. Deadline: Noon Nov. 13, 2020.

Recommended problems: 3.1*, 3.2, 3.3, 3.4, 3.7* and 3.8

Chapter 4: Non-relativistic strings.

Reading instructions: This rather easy chapter is an application of Lagrangian techniques to a specific field theory in 1+1 spacetime dimensions. The concept of string tension and the different kinds of boundary conditions are the crucial aspects here.

Home problem 4: Do BZ problem 4.5. Deadline: Noon Nov. 13, 2020.

Recommended problems: 4.1, 4.4* and 4.6.

Week 2 (46), 3 lectures: Chapters 5-10.

Relativistic theories for point particles and strings. The static gauge. Light-cone strings and fields.

Chapter 5: The relativistic point particle.

Reading instructions: Familiar Lagrangian techniques applied to the relativistic point-particle. The important aspects here are reparametrisation invariance and the charged particle action in eq. 5.34, with some extra comments in the Lecture notes.

Home problem 5: Do BZ problem 5.6. Deadline: Noon Nov. 20, 2020.

Recommended problems: 5.1, 5.2*, 5.3 and 5.7.

Chapter 6: Relativistic strings.

Reading instructions: Sections 6.1 - 6.4 should be studied carefully but describes basically just a rather straightforward generalisation of the relativistic point-particle. The same is true for the equations of motion and boundary conditions in sect. 6.5 but there are some important new features coming up when obtained the boundary conditions. The really new and very important point concerns choosing a reparametrisation gauge (i.e., choosing nice coordinates) which is addressed in sect. 6.6. Implications are discussed in sections 6.7 - 6.9 which should be understood in detail.

Home problem 6: Do BZ problem 6.7. Deadline: Noon Nov. 20, 2020.

Recommended problems: 6.1, 6.2* and 6.6.

Chapter 7: String parametrisation and classical motion.

Reading instructions: The main results here are given in eqs 7.26 - 7.32. The steps needed to derive these equations must be fully understood. Some consequences of these equations are studied in the rest of the chapter: For open strings in sect. 7.4 and closed ones in sect. 7. 5. Cosmic strings in sect. 7.6 is less important for the course but nice to know something about.

Home problem 7: Do BZ problem 7.5. Deadline: Noon Nov. 20, 2020.

Recommended problems: 7.1, 7.2 and 7.4*.

Chapter 8: World-sheet currents.

Reading instructions: This is again a rather easy chapter where many things should be familiar from previous courses like the Lagrangian, conserved currents etc. The new aspects concern the fact that there are two spaces involved: The world-sheet and the target spacetime! The last two sections are important: Lorentz algebra and the sloop parameter.

Home problem 8: Do BZ problem 8.7. Deadline: Noon Nov. 20, 2020.

Recommended problems: 8.1, 8.5* and 8.6.

Chapter 9: Light-cone relativistic strings.

Reading instructions: Important aspects are the light-cone solution to the constraints and the mode expansions. Sections 9.1 and 9.2 will be simplified a bit in the Lecture notes. All the results in the remaining sections 9.3 - 9.5 are crucial for the rest of the course!!!

Home problem 9: Do BZ problem 9.5. Deadline: Noon Nov. 27, 2020.

Recommended home problems: 9.1, 9.2 and 9.3*.

Chapter 10: Light-cone fields and particles.

Reading instructions: 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 in order to understand the spectrum of the string discussed in the coming chapters. The home problem will help you to isolate the most important point in this chapter.

Recommended problems: 10.2, 10.3* and 10.4.

Home problem 10: Do BZ problem 10.6. Deadline: Noon Nov. 27, 2020.

Week 3 (47), 2 lectures: Chapters 11-12

Quantisation of relativistic point particles and open strings.

Chapter 11: The relativistic quantum point particle.

Reading instructions: This chapter is the start of the more intricate aspects of string theory, here examplified by point particles. The light-cone quantisation and the implementation of Lorentz invariance in the light-cone gauge (section 11.6) are a bit tricky but absolutely crucial features that must be understood in detail as preparation for the quantum string in the next chapter.

Home problem 11: Do BZ problem 11.6. Deadline: Noon Nov. 27, 2020.

Recommended problems: 11.1, 11.2 and 11.5*.

Chapter 12: Relativistic quantum open strings.

Reading instructions: This is one of the key chapters in the whole course! All sections must be understood in detail.

Home problem 12: Do BZ problem 12.6. Deadline: Noon Dec. 4, 2020).

Recommended problems: 12.1, 12.2, 12.3*, 12.4 and 12.7

Week 4 (48), 3 lectures: Chapters 13, 24 and beginning of Chapter 14, plus extra material in lecture notes

The closed bosonic and supersymmetric strings in light cone gauge. There is also a covariant version of this that will be discussed later.

Chapter 13: The relativistic quantum closed string.

Reading instructions: This is another chapter that you must understand in detail, including the related extra material in the Lecture notes.

Home problem 13: Do BZ problem 13.5. Deadline: Noon Dec. 4, 2020).

Recommended home problems: 13.1* and 13.2.

Chapter 24: The Polyakov formulation

Reading instructions: This is yet another chapter that you must understand in detail, including the related extra material in the Lecture notes. Some of the extra Lecture note material is rather advanced and should be viewed only as a brief introduction. The zoom-lecture will contain more information about how to approach this extra material.

No home problem (see project topics under part 2 below).

Chapter 14: Superstrings and M-theory (if there is time). Extra material in the lecture notes.

Reading instructions: This is the last chapter that you must understand in detail, including the related extra material in the Lecture notes. Some of the extra Lecture note material is rather advanced and should be viewed only as a brief introduction. The zoom-lecture will contain more information about how tp approach this extra material.

Home problem 14: Do BZ problem 14.3. Deadline: Noon Dec. 11, 2020.

Recommended home problems: 14.1, 14.2 and 14.4*.

Week 5 (49), 2 lectures: Continuation of Chapter 14 on superstrings and extra material in the lecture notes. Extra question session Friday at 10.00 (zoom).

Zwiebach Part II: Chapters 15 - 21 plus 23, one small project on a topic from either the chapters in Part II of BZ or from the list of slightly more advanced problems in the Lecture notes. For more details see the Lecture notes.

Week 6 (50), 2 lectures: Parts of Chapters 15 - 18.

Chapters 15 and 16: D-branes, gauge fields and charges.