530224 String theory (2015)

When: periods I and II.


The return date of the exam has been extended! It is on Wednesday Dec 16 (at 10:00).

The final exam is a home exam and will begin at 10am on Friday Dec 11.

Lectures (2 h/wk):

Lectures are held on Wednesdays at 12-14 in A315. (Previously they took place at 14-16 in D115.) Last lecture mid-Dec.

Lecturer: Niko Jokela (Physicum, A324)

Course material

We mainly follow the lecture notes by Esko Keski-Vakkuri & Fawad Hassan. The standard reference books in string theory are by Polchinski (vol 1 bosonic string and vol 2 superstring) and Green & Schwarz & Witten (two vols, bit old but beautiful).


Handwritten notes will appear here.

Lecture 1 (Sep 2): relativistic point particle and string, Nambu-Goto and Polyakov actions

Lecture 2 (Sep 9): symmetries of Polyakov action, gauge fixing, Noether currents, boundary conditions

Lecture 3 (Sep 16): light-cone coordinates, Hamiltonian analysis, classical Virasoro algebra, classical mass spectrum

Lecture 4 (Sep 23): guest lecturer E. Keski-Vakkuri; path integral quantization of the string, Faddeev-Popov trick, ghosts. Material Sec. 2.12 of Esko's notes as well as pages 160-165 of "Aspects of Symmetry" book by S. Coleman.

Lecture 5 (Sep 30): quantization of bosonic string, open string mass spectrum

Lecture 6 (Oct 7): Lorentz symmetry, covariant quantization, quantum Vir. algebra, closed string mass spectrum

Lecture 7 (Oct 14): conformal Killing equation, SL(2,C), 2d CFT, Ward identities

Lecture 8 (Oct 28): radial quantization, operator formalism

Lecture 9 (Nov 4): string scattering, Virasoro-Shapiro amplitude, Veneziano amplitude

Lecture 10 (Nov 11): strings in background fields

Lecture 11 (Nov 18): RNS action, R and NS boundary conditions, low-lying spectrum

Lecture 12 (Nov 25): modular invariance, closed string spectra

Lecture 13 (Dec 1): D=11 and D=10 SUGRA, RR-forms coupling to extended objects, black p-branes

Lecture 14 (Dec 9): KK-compactification, T-duality, S-duality

Exercises (2 h/wk):

Teaching assistant: Jarkko Järvelä (jarkko.jarvela@helsinki.fi, A313)

Time and place: Thursdays 16-18 in A315.

Here you can find exercises. Return date is on Tuesday. First exercise session on Thu Sep 10.


Problem set 1 (due Sep 8)

Problem set 2 (due Sep 15)

Problem set 3 (due Sep 23 by noon!)

Problem set 4 (due Sep 29)

Problem set 5 (due Oct 13)

Problem set 6 (due Oct 20)

Problem set 7 (due Nov 3)

Problem set 8 (due Nov 10)

Problem set 9 (due Nov 24)

Problem set 10 (due Dec 1)

Problem set 11 (last) (due Dec 8)


The final exam will be a home exam and starts on Friday Dec 11 at 10am.

Supplementary reading:

Check the string wiki web site, where a huge number of lecture notes/articles on various aspects on string theory can be found. A good pedagogical take can be found in those by David Tong.