Agnese Bissi: Analytic conformal bootstrap
Lecture plan:
I will discuss analytic techniques to study conformal field theories in space time dimensions greater than two.
Reading recommendations:
https://arxiv.org/abs/2202.08475
https://arxiv.org/abs/1805.04405
https://arxiv.org/abs/1703.00278
Yiming Chen: Quantum chaos in gravity and field theories
Lecture plan:
Lecture 1: Review of basics of black holes and ideas of holography. Derive black hole thermodynamics using Euclidean gravity path integral. General comments on what semiclassical gravity captures and the role of spacetime wormholes.
Lecture 2: Review of random matrix statistics in quantum systems, probe using spectral form factor. Discuss the double cone wormhole geometry in general dimensions. Discuss its one-loop determinant, connection to quasinormal modes and the notion of Thouless time.
Lecture 3 & Lecture 4: Review of BPS states and extremal black holes. Discuss the idea of BPS chaos. Propose BPS and near BPS states as a controlled playground to study chaos in quantum field theories. Discuss connections to the fortuity phenomenon of BPS states. Discuss explicit examples in the N=4 SYM theory and the D1D5 CFT.
Reading recommendations:
- “A semiclassical ramp in SYK and in gravity” by Phil Saad, Stephen Shenker, Douglas Stanford: https://arxiv.org/abs/1806.06840
- “BPS chaos” by Yiming Chen, Henry Lin, Stephen Shenker: https://arxiv.org/abs/2407.19387
Matthias Gaberdiel: AdS3/CFT2 duality
Lecture plan and reading recommendations:
As a preparation it would probably be most useful if students study a bit CFT2, in particular WZW models, and a good reference for that are Lorenz's lecture notes, see
https://www.conferences.itp.phys.ethz.ch/esi-school/Lecture_notes/WZW%20models.pdf
I will probably also cover some of that material in my course. I will then aim to cover (among others) aspects of the papers
The Worldsheet Dual of the Symmetric Product CFT, 1812.01007
Deriving the AdS3/CFT2 correspondence, 1911.00378
Free field world-sheet correlators for AdS3, 2009.11306
Beyond the tensionless limit: integrability in the symmetric orbifold, 2312.13288
Roman Lee: Multiloop Feynman integrals
Lecture plan:
Lecture 1: Introduction & Basics of Feynman integrals.
Lecture 2: Integration-by-parts (IBP) techniques.
Lectures 3 & 4: Differential equations & boundary condition evaluations.
Reading recommendations:
I. textbooks:
1. Weinzierl, S. (2022). Feynman Integrals: A Comprehensive Treatment for Students and Researchers. Springer Nature.
This is a contemporary voluminous textbook including many topics on multiloop integrals. A preprint version is available from https://arxiv.org/pdf/2201.03593
2.Haraoka Y. Linear differential equations in the complex domain //Suugaku Shobou, Tokyo. – 2015.
This is a contemporary textbook on Fuchsian theory of linear differential equations. The full text seems to be available from https://link.springer.com/content/pdf/10.1007/978-3-030-54663-2.pdf
II. papers:
1. Chetyrkin, K. G. and Tkachov, F. V. (1981). Integration by parts: The algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192: 159.
2. Kotikov, A. V. (1991). Differential equations method: New technique for massive Feynman diagrams calculation, Phys. Lett. B254: 158–164.
3. Remiddi, E. (1997). Differential equations for Feynman graph amplitudes, Nuovo Cim. A110: 1435–1452.
4. Tarasov, O. V. (1996). Connection between Feynman integrals having different values of the space-time dimension, Phys. Rev. D 54: 6479.
5. Baikov, P. A. (1997). Explicit solutions of the multiloop integral recurrence relations and its application., NIM in Phys. Res. A 389: 347.
6. Beneke, M. and Smirnov, V. A. (1998). Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522: 321–344.
7. Laporta, S. (2000). High precision calculation of multiloop Feynman integrals by difference equations., Int. J. Mod. Phys. A 15: 5087.
8. Henn, J. M. (2013). Multiloop integrals in dimensional regularization made simple, Phys.Rev.Lett. 110(25): 251601.
9. Lee, R. N. (2015). Reducing differential equations for multiloop master integrals, JHEP 04 (2015) 108.
10. Lee, R. N. (2021). Libra: A package for transformation of differential systems for multiloop integrals, Comput. Phys. Commun. 267: 108058.
Anna Tokareva: Unitarity constraints on effective field theories
Lecture plan:
Lecture 1: EFT concepts: field redefinitions, scattering amplitudes, unitarity
Lecture 2: Causality and analytic structure of scattering amplitudes, derivation of Martin-Froisssart bound, positivity bounds
Lecture 3: Constraints on EFT parameters from moments problem for positive-definite functions (EFThedron)
Lecture 4: Implications of full unitarity
Reading recommendations:
2412.08690
Dan Xie: Introduction to large language models
Xinyu Zhang: Supersymmetric localization
Lecture plan and reading recommendations:
1. Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories (arXiv: 9411210)
2. Localization techniques in quantum field theories (arXiv: 1608.02952)
Yunqin Zheng: Aspects of general symmetries
Wei Zhu: Introduction to Fuzzy Sphere Regularization
