Course Lectures
1. Basics of String Theory
Lecturer: Satoshi Nawata, snawata@fudan.edu.cn
Prerequisites: Quantum Mechanics, Basic knowledge of quantum field theory
About the course:
The basic idea of String Theory is that elementary particles are excitations of a string. Each quantum excitation of the string behaves like an elementary particle, and closed strings have a massless spin-2 particle in their spectrum, which made string theory a promising candidate for a quantum theory of gravity. It has also been remarkably successful as a theoretical framework capable of influencing other fields of physics and mathematics.
This course will introduce the basics of string theory. String theory is very broad, and it is still rapidly developing. Therefore, it is impossible to cover all the topics within six lectures. However, we will study selected basic topics.
• Quantizations of bosonic strings and D = 26
• Basics of 2d CFT
• Quantizations of superstrings and D = 10
• Type IIA/IIB theory
• D-branes
• Introduction to AdS/CFT correspondence
Main references:
Polchinski, String Theory I, II
S. Nawata, R. Tao, D. Yokoyama, Fudan lectures on string theory, [arXiv:2208.05179]
Lecture notes by Kazuo Hosomichi, available on his website.
David Tong, String theory [arXiv:0908.0333]
Supplementary references:
There are too many references on string theory. I just list the famous books on string theory:
• Green, Schwarz and Witten, Superstring Theory I, II
• Becker, Becker, Schwarz, String Theory and M-Theory: A Modern Introduction
• Zwiebach, A First Course in String Theory
For more information, you can refer to this website.
2. Basics of inflation and cosmological collider
Lecturer: Siyi Zhou (周思益)
About the course:
This is an introductory course for undergraduate student and master students to get familiar with the basics of inflation. It includes the basic picture of cosmology, field theoretical description of the inflaton field that drives inflation, some observations. In the end, I will introduce the basic idea of cosmological collider physics which is the main interest of my research currently.
3. Gravitational wave cosmology
Lecturer: Fa Peng Huang (黄发朋)
Syllabus:
1. Basics of cosmology and gravitational wave prob
2. Gravitational wave radiation and Einstein quadruple formula
3. Gravitational wave from cosmic string and other cosmic defects
4. Gravitational wave from binary stars
5. Gravitational wave from cosmic phase transition and inflation
6. Gravitational wave signals of dark matter and baryogenesis
Recommended books:
Gravitational Waves Volume 1 and Volume 2 by Michele Maggiore
4. Cosmological perturbation theory
Lecture: Xian Gao (高显)
Syllabus:
1. Basic concepts of perturbation theory
2. Metric and matter perturbations
3. Gauge transformation and gauge-invariant variables
4. Linearization of Einstein’s equations
5. Quadratic action for perturbations
6. Tensor perturbations and gravitational waves
7. Quantum fluctuations of a scalar field in de Sitter space
8. Power spectrum of curvature perturbation
9. Power spectra of gravitational waves
10. In-in formalism for cosmological correlation functions
11. Nonlinear perturbations
Reading Recommendations:
• V. Mukhanov, H. Feldman and R. Brandenberger, Theory of cosmological perturbations, Phys. Rept. 215 (1992) 203.
• A. Riotto, Inflation and the theory of cosmological perturbations, arXiv: hepph/0210162.
• K. Malik and D. Wands, Cosmological perturbations, arXiv: 0809.4944.
• D. Baumann, TASI Lectures on Inflation, arXiv: 0907.5424.
5. Celestial Holography
Lecture: Wenjie Ma (马文杰)
Reference: Lectures on Celestial Holography, arXiv: 2107.02075
6. Dark Matter
Lecture: Yiming Zhong (钟益鸣)
Lecture notes: Introduction to Dark Matter and Dark Sector Models and Searches
Individual Lectures
1. Evidence of Dynamical Dark Energy
Lecturer: Qinxun Li (李秦埙)
Abstract: Dark energy is a negative pressure ingredient which produces the recent accelaration of cosmic expansion. Cosmological constant ($\Lambda$) is the simpliest dark energy model , but it successfuly explained most observational phenomenons, especially the cosmic microwave background. In this standard model of cosmology, dark energy has constant energy density. However, recent results of the DESI(Dark Energy Spectroscopic Instrument) collaboration reveil a 3-4.2 sigma evidence of dynamical dark energy, which means that the energy density of dark energy is not constant but varies with time. Moreover, the observation data prefer a werid behavior of dark energy evolution, which requires a violation of the null energy condition. The high energy and gravity communities have very diverse opinions on this result. I contributed significantly to both the analysis and interpretation of the DESI results, and I will present the principles of the analysis and discuss the nature of evidence, potential issues, and alternative explanations.
Biography: I am a second year PhD student at the University of Utah, working on observational cosmology. My research focuses on understanding the systematics of large-scale structure probes. I am also interested in weak gravitational lensing and galaxy-halo connection, and test of modified gravity. I got my bachelor degree from University of Science and Technology of China (USTC) in 2023.
2. Road to quantum universe: An introduction to de Sitter holography
Lecturer: Wenqi Yu (余文琪)
Abstract: AdS/CFT, or gauge/gravity duality, as the most successful attempt at a quantum gravity theory to date, provides profound insights into many aspects of quantum gravity—such as how information escapes from the most extreme objects in nature: black holes. One of its core concepts is the emergence of bulk spacetime. In the case of AdS, its hyperbolic geometry can be viewed as emerging from the flat spacetime of the boundary, with the AdS radius corresponding to the energy scale of the boundary field theory. When the radius approaches infinity, the boundary theory flows to a UV fixed point, namely, a conformal field theory.
However, our real universe—along with its inflationary origin—has positive spacetime curvature and is believed to approximate de Sitter (dS) spacetime. Can the successful framework developed for AdS be extended to dS? If achievable, this would significantly advance our understanding of the quantum origin of our universe.
In this talk, I will discuss several aspects of dS holography:
1. The dS Dictionary: Partition Functions and Operator Correspondence
This aspect is linked to the calculation of cosmological correlation functions. Techniques like the cosmological bootstrap arise from constraints imposed by boundary conformal symmetry. However, I will demonstrate that the dS dictionary differs significantly from that of AdS.
2. Holographic Renormalization in dS and the Emergence of Time
This section will explore how time emerges in the dS framework and the role of holographic renormalization.
3. Dynamical Gravitational Effects in dS Spacetime
I will discuss gravitational dynamics in dS spacetime, a topic initially explored by Hartle and Hawking in their work on the wave function of the universe and its quantum origins. Recent progress in low-dimensional quantum gravity models has led to new developments in this direction.
Biography: Wenqi Yu is current a second year PhD student at the Hong Kong University of Science and Technology. He obtained BS degree at University of Science and Technology of China in 2023. His research interests include quantum cosmology and blackhole physics.
3. Boostrapping the primordial sky: wave functions, symmetries and the unitarity
Lecturer: Xiangwei Wang (王祥苇)
Abstract: It is widely believed that the seeds of all structures that constitute our current universe originate from a phase of cosmic inflation, where quantum effects interplay with gravity significantly. One important feature of inflationary physics is that all what we can make use of are in-in cosmological correlators living on the future boundary of the inflationary spacetime rather than in-out scattering amplitudes for flat spacetime particle physics. In this talk, I shall present recent developments for calculating and constraining these correlators, emphasizing symmetry principles and fundamental quantum constraints. We begin with the wave functional formalism, which provides a direct link between the initial quantum state of the universe and late-time observable correlations. Central to our discussion is the cosmological bootstrap programme, utilises consistency requirements—such as unitarity), locality, and de Sitter symmetries—to "bootstrap" the form of correlators, often bypassing detailed dynamical calculations. A key development within this framework is the boostless bootstrap, where richer phenomenology can be introduced at the cost of violating boost symmetries.
Reference: 1811.00024, 2203.08121, 2205.00013, 1503.08043, 2010.12818, 2009.02898
Biography: Mr. Xiangwei Wang graduated with both a BA and a Msci degree from the Cavendish Laboratory, University of Cambridge, in year 2024. He conducted research on modified gravity under the supervision of Dr. William Barker, Dr. Amel Durakovic and Dr. Tobias Mistele for his master thesis. At the moment, he is working on theoretical cosmology and quantum field theory in curved spacetime, supervised by Prof. Yi Wang and Dr. Donggang Wang, as a research assistant at the Hong Kong university of Science and Technology.
4. Complexity, scaling, and a phase transition
Lecturer: Jiayue Yang (杨佳悦)
Abstract: We investigate the holographic complexity of CFTs compactified on a circle with a Wilson line, dual to magnetized solitons in AdS4 and AdS5. These theories have a confinement-deconfinement phase transition as a function of the Wilson line, and the complexity of formation acts as an order parameter for this transition. Through explicit calculation, we show that proposed complexity functionals based on volume and action obey a scaling relation with radius of the circle and further prove that a broad family of potential complexity functionals obeys this scaling behavior. As a result, we conjecture that the scaling law applies to the complexity of conformal field theories on a circle in more general circumstances.
Biography: 杨佳悦，现为加拿大滑铁卢大学应用数学专业的博士生，师从国际著名引力与相对论专家，加拿大物理学会前主席Robert Mann教授。杨佳悦2022年本科毕业于吉林大学唐敖庆班物理专业并获得了院长奖学金；2024年硕士毕业于加拿大滑铁卢大学物理与天文系。她的研究兴趣广泛，涵盖高能物理和引力物理，尤其专注于黑洞热力学、量子信息及全息理论，在JHEP和PRD等期刊上发表论文6篇。此外，她对教学和科学传播充满热情，在其哔哩哔哩频道悦悦爱物理上积累了超过13,000名粉丝。
5. Adiabatic Vacuum
Lecturer: Junqi Zhang (张骏祺)
Abstract: In curved spacetime, the construction of a vacuum state presents a subtle challenge, primarily due to the general absence of time translational symmetry that is characteristic of flat spacetimes. Nevertheless, in typical cosmological setups, the high symmetry of the spacetime often allows for a preferred approach to constructing the adiabatic vacuum when time translational symmetry is approximately preserved. In this talk, I will introduce the motivation and formalism of the adiabatic vacuum at intuitive level, as well as its applications in cosmological problems such as particle production.
Biography: I am an incoming PhD student at University of Wisconsin-Madison. I obtained BS degree at University of Wisconsin-Madison in 2025. My primarily research interest is the interface of cosmology and particle physics phenomenology, specifically exploring the early universe’s history by studying high-energy processes through observable relics.
6. A Short Introduction to Swampland Program and String Cosmology
Lecturer: Junkai Wang (王俊凯)
Abstract: String theory is, at present, humanity’s only known Theory of Everything (TOE) that is simultaneously the most hopeful, well-controlled, and ultraviolet-complete. This naturally raises the question: beyond the Standard Model and particle physics, can string theory also describe macroscopic phenomena such as gravity and cosmology? The problems of “how to obtain our universe from string theory” and “how to obtain our Standard Model from string theory” are of comparable importance.
On the other hand, Wilsonian effective field theory tells us that low-energy physics decouples from high-energy physics, while string theory intrinsically resides at extremely high energy scales. Why, then, should we expect it to say anything about low-energy quantum field theory or contemporary cosmology? The string-inspired Swampland conjectures provide powerful constraints on quantum field theory and, over the past two decades, have continually reshaped our understanding of QFT from many perspectives.
In this talk, I will briefly introduce topics related to the Swampland conjectures and string cosmology. Audience members are expected to have prior knowledge of quantum field theory. Reconmended references are arXiv:2212.06187 and arXiv:2303.04819. For those interested in dark energy and the late-time universe, it is encouraged to watch Qi-Xun Li's lecture beforehand.
