2024/2025
Research Seminar "Integrability in Quantum Field Theory 2"
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Open to:
students of all HSE University campuses
Instructors:
Mikhail Alfimov
Language:
English
ECTS credits:
6
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. In the second part of the course there will be given an introduction into the applications of the theory of integrable systems to the study of the spectrum of $\mathcal{N}=4$ supersymmetric Yang\Ч Mills theory and dual superstring theory on the $\text{AdS}_5\times\text{S}^5$ background and we will study integrable deformations of sigma models. The course is intended for PhD and Master students. Postdocs and Bachelor students are also welcome.
Learning Objectives
- Study examples of integrable quantum field theories: Bose gas model and Principal Chiral Field.
- Study AdS/CFT correspondence with the example of AdS_5 x S^5 string background.
- Get acquainted with classically integrable sigma models.
Expected Learning Outcomes
- Able to transform the Y-system for N=4 SYM into the T-system and solve it.
- Can obtain AdS_5 x S^5 superstring theory worldsheet S-matrix from Zamolodchikov-Faddeev algebra.
- Familiar with examples of calculation of the characteristics of the N=4 SYM spectrum using the Quantum Spectral Curve method.
- Knows how to derive the Quantum Spectral Curve equations for N=4 SYM and AdS_5 x S^5 superstring theory.
- Studied the notion of integrable deformation of sigma models and learned several examples of such models including O(N) models and others.
- Understands the 1-loop integrability of N=4 SYM, asymptotic spectrum and Thermodynamic Bethe Ansatz equations of this theory.
Course Contents
- Integrable structure of N=4 SYM.
- Y- and T-system for the spectrum of N=4 SYM.
- Quantum Spectral Curve for N=4 SYM and AdS_5 x S^5 superstring.
- Application of the QSC method for the SL(2) sector of N=4 SYM.
- S-matrix for the AdS_5 x S^5 superstring.
- Integrable deformations of sigma models.
Interim Assessment
- 2024/2025 4th moduleGiving talk at the seminar*0.7+Taking part in the discussion at the seminar*0.3
Bibliography
Recommended Core Bibliography
- Ahn, C., & Nepomechie, R. I. (2010). Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix. https://doi.org/10.1007/s11005-011-0478-9
- Gromov, N., Kazakov, V., Leurent, S., & Volin, D. (2011). Solving the AdS/CFT Y-system. https://doi.org/10.1007/JHEP07(2012)023
- Gromov, N., Kazakov, V., Leurent, S., & Volin, D. (2013). Quantum spectral curve for AdS_5/CFT_4. https://doi.org/10.1103/PhysRevLett.112.011602
- Gromov, N., Kazakov, V., Leurent, S., & Volin, D. (2014). Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$. https://doi.org/10.1007/JHEP09(2015)187
- Minahan, J. A., & Zarembo, K. (2002). The Bethe-Ansatz for N=4 Super Yang-Mills. https://doi.org/10.1088/1126-6708/2003/03/013
- V. A. Fateev, & A. V. Litvinov. (2018). Integrability, duality and sigma models. Journal of High Energy Physics, 2018(11), 1–29. https://doi.org/10.1007/JHEP11(2018)204
Recommended Additional Bibliography
- A. V. Litvinov, & L. A. Spodyneiko. (2018). On dual description of the deformed O(N) sigma model. Journal of High Energy Physics, 2018(11), 1–29. https://doi.org/10.1007/JHEP11(2018)139
- Rej, A. (2009). Integrability and the AdS/CFT correspondence. https://doi.org/10.1088/1751-8113/42/25/254002