String Theory - Spring 2007

Jan de Boer & Amir-Kian Kashani-Poor
First class: Wednesday February 7
No class: Wednesday March 28
Last class: Wednesday May 23
Question session: Wednesday May 30, 10.00
Written Exam: Wednesday June 6, 10.00-13.00
lecture times: Wednesdays 10.00-13.00
room: P0.17
(you can find the buildings on this map)
credits: 6EC

This course consists of a basic introduction to string theory. The course will more or less follow the book Becker, Becker, Schwarz, String Theory and M-Theory (Cambridge University Press, 2007). (Can also be ordered at bol.com). Below I will keep track of the topics covered each week, so that you can see where we stand in the class. There are several books about string theory, and there is a lot of material available on the web, so it shouldn't be too hard to find additional background material. Two books worth mentioning are

Green, Schwarz, Witten, Superstring Theory (two volumes) (Cambridge, 1987).

J. Polchinski, String Theory (two volumes) (Cambridge, 1998).

The course will contain various exercises. We will discuss these in class. Once every three weeks or so a set of exercises will be given which should be handed in. They will be graded, and completing these successfully can yield an upgrade of the final mark on the written exam.

February 7: page 17-25. Suggested reading: Chapter 1. Exercises: 2.1, 2.3, 2.5

February 14: page 26-35. Exercises: 2.6, and verify equations (2.51) and (2.52)

February 21: page 36-47. Exercises: verify (2.67) and (2.68); check the computation on page 46; problem 2.1.

February 28: remainder of chapter 2. Exercise: write down the most general state in the open string at oscillator level one and find the conditions for this to be (i) physical and (ii) spurious; Take home set 1 (ps, pdf); extra takehome problem (ps, pdf).

March 7: Schellekens, Introduction to Conformal Field Theory (ps, pdf), page 1-23. Exercises: identify the conformal group in d>2 by working out the commutation relations of the generators (2.11); generalize (2.7) to arbitrary metric; work through page 6,7; in Becker-Becker-Schwarz: 3.1, 3.2.

March 14: Schellekens, page 24-30, 33, 41-44. Exercises: prove Wick's theorem by induction; work out R(T(z)T(w)) and R(T(z) exp(i k X(w))); derive the general form of the 3-point function.

March 21: roughly Polchinski, sections 4.2, 4.3. Exercises: work out how g^{1/2} R transforms under Weyl transformations in 2d; work out the relation between the Ricci scalar and the Riemann tensor in 2d; demonstrate the BRST invariance of the action S_1 + S_2 + S_3 (given on page 126 in Polchinski).

April 4: finished Polchinski, section 4.3; sections 3.5, beginning of 6.6; Becker-Becker-Schwarz, section 3.4. Exercises: take home set 2 (ps, pdf), to be handed in on April 11.

April 11: finished Polchinski, section 6.6; introductory pages of Green-Schwarz-Witten; a selection of Polchinski, section 3.7. Exercises: determine poles of Virasoro-Shapiro amplitude in u, t, and s-channel by considering the integration region around 0, 1, and infinity, respectively; complete proof of PSL(2,C) invariance of VS amplitude; find the PSL(2,C) transformation that maps 3 arbitrary points of the complex plane to 0, 1, and infinity; express the Mandelstam variables in terms of CMS energy and scattering angle in the s-channel.

April 18: pages 109-112 and 118-125, exercises 4.2, 4.3, 4.6, 4.7

April 25: pages 126-138, problems 4.1, 4.2, 4.3, 4.7, 4.8

May 9: pages 187-198; homework (ps, pdf).

May 16: Polchinski on effective actions in sections 6.5, 6.6, 3.7. Exercises: take home set 3 (ps, pdf), to be handed in on May 23.