2025 (Current Year) Faculty Courses School of Science Department of Physics Graduate major in Physics
Advanced Special Lectures in Physics VI
- Academic unit or major
- Graduate major in Physics
- Instructor(s)
- Yasuaki Hikida
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Intensive
- Class
- -
- Course Code
- PHY.T635
- Number of credits
- 100
- Course offered
- 2025
- Offered quarter
- 2Q
- Syllabus updated
- Jul 2, 2025
- Language
- English
Syllabus
Course overview and goals
In the path integral formulation of quantum theory, complexifying the integration contour can sometimes render the integral convergent. When this idea is applied to quantum gravity, complexified geometries emerge as saddle points.
A well-known example of such complexified geometry appears in the context of the no-boundary proposal for the creation of the universe from "nothing." The choice of integration contour ultimately reduces to the question of which geometries are physically realized.
In recent years, intensive research on admissible complexified geometries
has been conducted by Kontsevich, Segal, Witten, and others.
This course aims to explain these developments and introduce related research based on the gauge/gravity correspondence.
Course description and aims
To understand the general framework of path complexification in the path integral formulation of quantum theory.
To deepen insight into the issues that arise when this idea is applied to quantum gravity, and how these issues may be resolved.
Keywords
path integral, complexified geometries, gauge/gravity correspondence
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The lecture is given in a form of intensive course in English.
Scheduled on 9/8(Mon), 9/9(Tue), 9/10(Wed).
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Path integrals and the method of complexification | To be specified during the lecture |
| Class 2 | Complexification in geometry | To be specified during the lecture |
| Class 3 | Concrete examples of complexified geometry | To be specified during the lecture |
| Class 4 | Concrete examples of complexified geometry | To be specified during the lecture |
| Class 5 | Complex saddles in Liouville theory | To be specified during the lecture |
| Class 6 | Analytic continuation and the Stokes phenomenon | To be specified during the lecture |
| Class 7 | Complexified geometry via gauge/gravity correspondence | To be specified during the lecture |
Study advice (preparation and review)
Textbook(s)
Unspecified
Reference books, course materials, etc.
Unspecified
Evaluation methods and criteria
Evaluation will be based on a report.
Related courses
- PHY.Q433 ： Field Theory I
Prerequisites
None
Other
This is a second-quarter course; however, as it will be conducted during the summer vacation, the reporting of grades will be delayed. Please be aware that the grades will not be submitted in time for the September graduation assessment.