2020/2021
Научно-исследовательский семинар "Интегрируемость в квантовой теории поля 1"
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
1, 2 модуль
Преподаватели:
Алфимов Михаил Николаевич
Язык:
английский
Кредиты:
3
Контактные часы:
30
Course Syllabus
Abstract
This course is organized in the form of weekly seminars, where we are going to discuss the integrability structures appearing in quantum field theory. These structures nowadays are present in numerous examples, such as sigma models, supersymmetric gauge theories, string theories, gauge/string dualities, scattering amplitudes and correlation functions etc. As pedagogical examples of the integrable systems solved by the Bethe Ansatz method Bose gas and Principal Chiral Field models will be considered in the first part of the course together with the foundations of the AdS/CFT correspondence for the case of 4-dimensional superconformal gauge theory. The course is intended for PhD and Master students. Postdocs and Bachelor students are also welcome.
Learning Objectives
- Study the examples of integrable quantum field theories: the Bose gas model and the Principal Chiral Field model.
- Learn the AdS/CFT correspondence with the example of AdS_5 x S^5 superstring background.
- Become acquainted with the classically integrable sigma models.
Expected Learning Outcomes
- Can obtain the Asymptotic Bethe Ansatz equations, their thermodynamic limit and Thermodynamic Bethe Ansatz equations for the PCF model.
- Understands the transition from Y- to T-system and how to solve it.
- Able to solve the supergravity equations, which yield the AdS_5 x S^5 superstring background as a key element of one of the examples of AdS/CFT duality.
- Became aware of the notions of flatness condition, monodromy operator and quasimomenta together with the conserved charges and their analytic structure.
- Knows how to derive Bethe Ansatz equations, their thermodynamic limit and Thermodynamic Bethe Ansatz equations.
Course Contents
- The model of Bose gas.Bethe equations for the spectrum of the Bose gas model and their thermodynamic limit. Thermodynamic Bethe Ansatz (TBA) equations for the Bose gas model.
- Principal Chiral Field (PCF) Model.Asymptotic Bethe Ansatz for the spectrum of the PCF model and their thermodynamic limit. Thermodynamic Bethe Ansatz equations for the PCF.
- Y- and T-system (Hirota equations) for PCF.Wronskian solution of the Hirota equations.
- AdS/CFT correspondence.String background AdS_5 x S^5 as a solution of supergravity equations.
- Classical integrability of sigma models.Classical integrability of the PCF model and AdS_5 x S^5 superstring sigma model.
Interim Assessment
- Interim assessment (2 module)0.7 * Устный доклад на семинаре + 0.3 * Участие в дискуссии на семинаре
Bibliography
Recommended Core Bibliography
- Gromov, N. (2017). Introduction to the Spectrum of N=4 SYM and the Quantum Spectral Curve.
- Gromov, N., Kazakov, V., & Vieira, P. (2008). Finite Volume Spectrum of 2D Field Theories from Hirota Dynamics. https://doi.org/10.1088/1126-6708/2009/12/060
- Gromov, N., Kazakov, V., Sakai, K., & Vieira, P. (2006). Strings as Multi-Particle States of Quantum Sigma-Models. https://doi.org/10.1016/j.nuclphysb.2006.11.018
- Korepin, V. E., Izergin, A. G., & Bogoliubov, N. M. (1993). Quantum Inverse Scattering Method and Correlation Functions.
- Tseytlin, A. A. (2010). Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions.
Recommended Additional Bibliography
- Kazakov, V. (2018). Quantum Spectral Curve of $\gamma$-twisted ${\cal N}=4$ SYM theory and fishnet CFT. https://doi.org/10.1142/S0129055X1840010X