PHY2406S: String Theory

New Info March 11th

On March 20th I will be out of town. Unfortunately I will now be unable to hold the make-up lecture on March 14th. Check back next week for an update on future lectures.

Lecture Notes

• 09 Jan: Introduction and Overview
• 16 Jan: The classical string
• 23 Jan: Quantizing the string and Conformal Field Theory (CFT)
  [ Extras: Notes on the OPE in QFT , Notes on the conformal group and AdS ]
• 30 Jan: Calculating the critical dimension using CFT - using the Fadeev-Popov procedure
  [ Extras: Notes on the Feynman Path Integral formulation of QM ]
• 06 Feb: (b,c) systems, BRST operator and physical states, Vertex operators, 4-point tachyon scattering at tree level.
• 13 Feb: Closed string partition function , Chan-Paton factors, oriented and unoriented open strings , T-duality for closed and open strings . [ Extras: Affine Lie Algebras , Lie Algebras ]
• 20 Feb: break week, no lecture
• 27 Feb: Orbifolds and Orientifolds , Superstrings - Type I: worldsheet fermions, Ramond and Neveu-Schwarz sectors, supersymmetry, superghosts, critical dimension, massless spectrum .
• 06 Mar: Superstrings and Green-Schwarz anomaly ancellation - Type I, Type IIA, Type IIB, and the E₈xE₈ and SO(32) heterotic theories.
• 13 Mar: no lecture
• 20 Mar: strings in background fields: beta-functions
• 27 Mar: the Dp-brane and Op tensions; forces between D-branes, forces between Dp-branes and Dq-branes; mention of ADHM / D(p-4) as instantons inside Dp
• 03 Apr: compactification on Calabi-Yau manifolds
• 10 Apr: Duality I
• 17 Apr: Duality II

Other Notes

• A classic paper on superstrings is Friedan, Martinec and Shenker.
  Geometry useful for string theory is in Eguchi, Gilkey and Hansen, Physics Reports.
  How to do group theory, including tables of representations and how to find Clebsch-Gordan coefficients and transformations under subgroups is in Slansky, Physics Reports.
• Paul Ginsparg wrote a very comprehensive set of notes on CFT and its applications, for his Les Houches Lectures 1988
• Michael Peskin has a set of elementary lectures on CFT and string perturbation theory in his TASI-86 lectures (PDF, 10.3MB)
• For lecture notes on black holes and black branes in string theory, including a lot about entropy, see my TASI-99 notes (PDF, 0.582MB) .
• Antoine van Proeyen has a nice review on supergravity, including an introduction to spinors in diverse dimensions (this is also in a Polchinski appendix!); see Structure of Supergravity Theories (PDF, 0.304MB)
• Superspace, or 1001 Lessons in Supersymmetry (PDF, 3.03MB) - a newly-online book by Jim Gates, Marc Grisaru, Martin Rocek and Warren Siegel. Contains "all you ever wanted to know about SUSY but were afraid to ask".

Texts

Johnson's book has a new erratum webpage that you should consult if you own his book.

The gold-standard texts in this field are String Theory (two volumes) by Polchinski and Superstring Theory (two volumes, older) by Green, Schwarz and Witten. But the book I really like is an excellent brand-new textbook D-Branes by Clifford Johnson on which I will be loosely basing the course. Serious string theory students should buy all five, but Johnson and Polchinski should be priorities. All of these texts are published by Cambridge University Press.

Polchinski and GSW are on reserve / short-term loan in the Physics Library; most are also in Gerstein too (but someone apparently stole the first volume of one two-volume set...!). Johnson's book will be on reserve in the Physics Library, and it is available at the campus bookstore.

Note that I will not be lending out any personal copies of any of these five textbooks at any time during the semester.

Syllabus

Topics covered will be introductory and will include the following.

Perturbative string theory

Polyakov action, covariant and BRST quantization, conformal field theory.

Strings in background fields

The sigma-model, alpha-prime and g-string expansions, beta-functions.

D-branes a la Polchinski

Open string boundary conditions, D-branes, forces between D-branes.

Compactification

Circle compactification, Calabi-Yau manifolds.

Duality

T-duality, S-duality [Matrix Theory, Gravity/Gauge Correspondence].

Prerequisites and Assessment

Students taking this course for credit should have first-semester Quantum Field Theory (Physics style) and General Relativity (either Physics or Math style) under their belts. For Physics and CITA students I also reckon it will be necessary to take second-semester Quantum Field Theory concurrently. However, if you want to take my String Theory course for credit, but have a problem with these prerequisites (e.g. you've taken QFT elsewhere), call me at 8-3911 or drop by and make an appointment to chat about it. Auditors can of course come with whatever preparation level they like, but it would be wise to know e.g. what a geodesic and a loop diagram are...

The grading scheme is that 90% will be based on special topic presentations at the end of the semester, and 10% on class participation. I will examine the final project presentations after classes have finished, so as not to fall afoul of regulations. If anyone needs me to avoid specific days/times for religious/similar reasons, please let me know. Thank you for your cooperation.

Topics for final project presentations:

• Gao: Black hole entropy in string theory
• Khavkine: Non-commutative gauge theory
• Saremi: AdS/CFT correspondence and RG flow
• Vaudrevange: graviton scattering in [QFT and] string theory

For other important deadlines and dates, see the Faculty of Arts and Sciences Calendar .