Introduction to String Theory, Part 2

Course Instructor: Hirosi Ooguri , the Fred Kavli Professor of Theoretical Physics and Mathematics and the Director of the Walter Burke Institute for Theoretical Physics.

• Lectures: 9:00 - 10:30 on Mondays and Wednesdays, beginning on March 31 and ending on May 28.
• Starting on February 12, the class will meet at 269 Lauritsen.
• Office Hours: 10:30 - 11:00 on Wednesdays after the class. Students can also make appointments with me as needed.

Course Description:

Prerequisites: Ph 205 or equivalent.

• Ph 250 A will cover the worldsheet formulation of string theory, including conformal field theory, supersymmetry, the emergence of gravity, scattering amplitudes, T-duality, and D-branes. We will also discuss how to build semi-realistic models of elementary particle physics from string theory.
• Ph 250 B will cover advanced topics such as non-perturbative dualities, Calabi-Yau geometry and mirror symmetry, black holes, the holographic principle and its relation to quantum information theory, and constraints on gravitational theories.

Course Announcement:

We will miss two classes, on April 14 and 16. Make-up classes will be announced later.

Course Diary:

Reading Recommendation: For the first half of this quarter, I recommend Part 1 and Part 2 of Mirror Symmetry (Clay Mathematics Monographs Volume 1, 2003).

03.31: discussed compactification of 10-dimensional supergravity and the conditions for the compactification to preserve supersymmetry, covariantly constant spinors, and Berger's classification of irreducible holonomies.

• We will make use of ideas from differential geometry such as differential forms, cohomology, characteristic classes and index theorems. This YouTube playlist of my course on geometric methods in physics may be useful.
• You can also download my lecture notes on geometric methods in physics from this webpage (Caltech access is required).

04.02: discussed Calabi-Yau geometry and examples of Calabi-Yau manifolds in one, two and three complex dimensions. We started to discuss the moduli space of complex structure and complexified Kahler structure of Calabi-Yau manifolds.

04.05: discussed the moduli space of Calabi-Yau manifolds. Using the Torelli-type theory, the special Kaehler geometry of the complex structure moduli space was derived. We also discussed toric geometry as an example of non-compact Calabi-Yaus.

As a supplement to the lectures on April 2 and 5, I recommend chapters 5, 6, and 7 of Mirror Symmetry.

Lecture Videos: posted on this YouTube playlist.

Reading Materials:

• The course in the winter quarter was based mostly on this lecture note.
• For the first half of this spring quarter course, I recommend Part 1 and Part 2 of Mirror Symmetry (Clay Mathematics Monographs Volume 1, 2003).
  
• Chapters 12 ~ 16 of Superstring Theory: Loop Amplitudes, Anomalies and Phenomenology, Vol. 2 by Michael B. Green, John H. Schwarz, Edward Witten are also excellent and highly recommended.
• Here is my lecture note about topological string theory based on the course I gave at the Institute for Advanced Study. The first 7 pages or so are about Calabi-Yau geometry in general, which I used in the first week of this quarter. Here is the YouTube playlist of the lectures.
  
• Here is my lecture note on complex manifolds and Kaehler manifolds.
  

Final Presentations:

Registered students should give final presentations in the last two class meetings. Each student will have 15 minutes including Q&A. Topics of the final presentations can be anything you found interesting about gauge theory or symmetry in quantum field theory. Please discuss with other students of the class so that different topics are chosen. Jaeha Lee will schedule and coordinate your presentations. You can use either the black board or the projector. In the latter case, please send your presentation files to him so that he can set them up on his PC.

Please fill out the spreadsheet to coordinate the final presentation schedule:

Here are some examples you may consider, but you can choose different topics if you prefer:

References:

String Theory

• Superstring Theory: Loop Amplitudes, Anomalies and Phenomenology, Vol. 2 by Michael B. Green, John H. Schwarz, Edward Witten
• String Theory, Vol. 1 and 2 by Joseph Polchinski

Conformal field theory

• Infinite conformal symmetry in two-dimensional quantum field theory by A. A. Belavin, A. M. Polyakov, A.B. Zamolodchikov
• TASI lectures on the conformal bootstrap by David Simmons-Duffin
• ICTP lectures on conformal field theory by Zohar Komargodski

Topological field theory

• Mirror symmetry, part 2

AdS/CFT correspondence

• Large N field theories, string theory and gravity by O. Aharony, S.S. Gubser, J. Maldacena, H. Ooguri, Y. Oz
• TASI lectures on the emergence of the bulk in AdS/CFT by Daniel Harlow
• The entropy of Hawking radiation by Ahmed Almheiri, Thomas Hartman, Juan Maldacena, Edgar Shaghoulian, Amirhossein Tajdini