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Hirosi Ooguri
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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 have a make-up class on May 9 (Friday) at 9:00 - 10:30 at 269 Lauritsen.

The class on May 14 (Wednesday) is cancelled.

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.

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.

04.07: discussed the relation between classical equations of motion of string theory and the conformal invariance of the worldsheet theory. We saw why the Calabi-Yau condition is required by conformal invariance.

04.21: introduced the Witten index and studied a quantum mechanical example. The lecture on April 21 is based on this lecture note. I also recommend you to read this historical paper: E. Witten, "Supersymmetry and Morse Theory," J. Diff. Geom. 17 (1982) 661.

04.23: Calculated the Witten index of the 2d supersymmetric sigma-model in three different ways. In the first way, the Witten index is expressed as a sum over stationary points of any smooth function (a Morse function) on the target space M of the sigma model. In the second way, the Witten index is identified as a sum of the Betti numbers (with signs), i.e., the Euler number. In the third way, the Witten index is given as an integral of a monomial of the Riemann curvature. The fact that these three expressions all give the same Witten index is related to the Morse theory and the Index Theorems.

04.28: Discussed the Calabi-Yau compactification of the heterotic string. Explained the Green-Schwarz mechanism of the anomaly cancellation and the resulting restriction on the gauge field on the Calabi-Yau. Reading recommendation: The original 1984 paper by Candelas, Horowitz, Strominger, and Witten is still one of the shortest and most pedagogical introduction to the Calabi-Yau compactification of the heterotic string.

04.30: The Calabi-Yau compactification of the E8 x E8 heterotic string lands on the E6 SUSY GUT in four dimensions, where the number of generations is half the Euler characteristic of the Calabi-Yau manifold.

05.05: Discussed the antisymmetric tensor gauge fields in the Ramond-Ramond sector of type IIA and IIB string theories and the supergravity solutions that carry their charges.

05.07: Defined D-branes in type IIA and IIB strings and calculated the forces between them. Discussed their transformation under the T-duality.

05.09: After describing D-branes in Calabi-Yau manifolds, we started to discuss the AdS/CFT correspondence.

05.12: The rules of the AdS/CFT correspondence are discussed, including the identification between particle states in AdS and primary fields in CFT. The holographic representation of local bulk operators was reviewed. It was pointed out that the representation leads to a puzzle, which will be resolved in the next lecture. As a preparation for it, we discussed aspects of the Shannon entropy.

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:

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

Conformal field theory

Topological field theory

AdS/CFT correspondence