PHY2406S

String Theory

String Theory is an integral part of modern high-energy theoretical physics. The aim of this course is to provide an accessible introduction to the string theory toolbox. It will be pitched to first-year graduate students, although more senior participants will also be warmly welcomed as auditors.

Announcements

Apr.12: marks have been submitted and final grades were also sent to you individually by email. Everyone got either a mid-high A or an A+. Well done -- you all kicked ass!
Apr.06: this is just a reminder that the final exam will be on Fri.10.Apr from 10am-1pm in MP1115. Each student gets a half-hour timeslot for their presentation.
Apr.02: all enrolled students received a detailed grade report of work done so far via email this afternoon. (Everyone did very well.) The only remaining graded works are HW4 and the final project presentations. Please remember that our Exam on April 10th will be held under full exam conditions (e.g. no cellphones). I suggest that you email me a static PDF file of your slides the night beforehand. If you prefer to use your own laptop, you must test it on the MP1115 equipment a few days in advance, in order to ensure that there are no compatibility problems. We will not have time for equipment troubleshooting during the exam timeframe. Anyone needing any last-minute help to finish the course is welcome: I can make time for you at short notice.
Apr.02: by majority class vote via email, the lecture will be held as scheduled tomorrow. Anyone without a building key should aim for the lobby of MP building at 11:00 and I will let you in.
Mar.25: as announced in class to those who bothered to show up, PDF notes for weeks 10-12 are available online by week number. Be warned that these are not nearly as well polished as the notes from Weeks 1-9 because I ran out of pain tolerance for typing the LaTeX. The notes are speech notes for me, which you may or may not find useful. week10, week11, week12.
Mar.04: notes are updated with the sigma model beta function material. Don't worry about the length of this section. I will focus on the main points and not get us lost in the rather long technical details.
Feb.27: notes are updated with T-duality, D-brane, and superstring duality material.
Feb.23: I would like enrolled students to please chat with me this week or next week about ideas for their final presentation project. Please make an appointment in person or by e-mail for guidance on topic choice and good sources for learning.
Feb.22: notes are updated with tomorrow evening's 6-8pm superstring material.
Feb.13: the final exam will be Fri.10.Apr from 10am-1pm in MP1115. Each student gets a half-hour timeslot for their presentation.
Feb.08: the notes are updated to contain material on BRST quantization of the bosonic string and tree level 3- and 4-point scattering amplitudes, to be discussed this Friday February 13th.
Feb.07: I will be away in San Diego on March 13 for a conference. The make-up class is scheduled for Mon.23.Feb 6-8pm in MP1115.
Feb.05: the lecture notes have been updated with tomorrow's lecture material.
Feb.01: Homework 1 is posted. The URL has been sent to students enrolled in the course by e-mail.
Jan.24: I will continue to update the LaTeX lecture notes file (subject to availability) >>HERE<<. I have just added sections completing the canonical quantization story (I forgot to discuss spurious state decoupling last time!) and discussing light-cone gauge quantization, modern path integral quantization and Fadeev-Popov ghosts, and starting to introduce conformal field theory.
Jan.24: Anyone who wants to consult my PHY2404S lecture notes on path integral quantization can find them here.
Jan.19: Cartoon for your amusement
Jan.17: New parts of the lecture notes are on the Virasoro algebra, mode expansions for classical open and closed strings, and canonical quantization.
Jan.16: The final exam (i.e., final project presentations by students taking the course for credit) is tentatively scheduled for Friday 10th April.
Jan.16: Three of our suggested textbooks are available to UofT students as free ebook downloads through the UofT Library: Blumenhagen, Luest and Theisen, Polchinski Vol.1 and Vol.2, Dine.
Jan.09: Lecture notes are posted for today and next week.
Jan.04: Our classes will be held on Fridays from 11am-1pm in MP1115, as advertised on the Physics Graduate website.

Syllabus

Nambu-Goto and Polyakov worldsheet actions, reparametrization invariance, conformal symmetry, Virasoro algebra
CFT basics: OPEs, currents, central charge, state-operator correspondence
Bosonic string: gauge fixing and $(b,c)$ ghosts, critical dimension
Superstring: $(\beta,\gamma)$ ghosts, the Ramond Neveu-Schwarz formalism; Heterotic string
D-branes and T-duality
Superstring duality
Vertex operators, Veneziano amplitude
The $\sigma$ model and its beta-functions as the equations of motion for spacetime fields
Compactification (eg Calabi-Yau manifolds, orientifold planes, orbifolds);
inflation, the string theory Landscape and the field theory Swampland
AdS/CFT: holography and applications to condensed matter and the QGP
Black hole entropy and the information paradox, black rings, fuzzballs, and firewalls

Assessment

4 homework assignments (15% each)
1 final project presentation (40%)

Texts

I will not require students to buy expensive technical textbooks, but I will recommend parts of the following texts (BLT especially) which should be helpful for students learning course material and carrying out their final projects.

Basic Concepts of String Theory, by Ralph Blumenhagen, Dieter Luest, and Stefan Theisen, 2013 (good for CFT beginners)
String Theory by Joseph Polchinski (two volume classic)
String Theory and M-theory by Katrin Becker, Melanie Becker and John Schwarz (strong on compactification)
Supersymmetry and String Theory by Michael Dine (strong on phenomenology applications)