Advanced Course on Integrability in the AdS/CFT Correspondence (2026 Spring Semester)

发布者：杨璐发布时间：2026-03-24浏览次数：18


Course Description

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The AdS/CFT correspondence is one of the most profound discoveries in theoretical physics, establishing a duality between certain gauge theories and string theory in anti–de Sitter space. In the planar limit, both sides of this duality become exactly solvable due to an underlying integrable structure.

This lecture series offers a systematic introduction to the role of integrability in AdS/CFT. Aimed at graduate students and young postdocs, the course covers the essential background: four-dimensional conformal field theory, string theory in AdS space, and Maldacena’s duality. We then explore how the one-loop dilatation operator of 𝒩=4 super Yang–Mills theory maps to the Heisenberg spin chain, and how classical string theory on AdS5×S5 gives rise to integrable sigma models. The final part introduces the asymptotic Bethe ansatz, the exact magnon S-matrix, and the dressing phase, leading to the modern understanding of the spectral problem.



Location: 15th Floor, Yifu Architecture Building, Campus, Southeast University, Nanjing [Tentative]

Time: Saturdays, 16:30–18:00 (Start Date: 28 March 2026) [Tentative]

Lecturer: Ryo Suzuki

Prerequisites: Background in quantum field theory, basic general relativity, and representation theory of Lie groups (especially SU(N)). No prior knowledge of string theory or integrable systems is assumed.

Additional Information: These lectures carry no academic credit. Lectures will be given in English. Please write an email to <ryosuzuki@seu.edu.cn> if you are interested in attending or have any questions.

Topics Covered

  • Crash course on string theory and the AdS/CFT correspondence

  • Classical and quantum integrability (Lax pairs, Yang–Baxter equation)

  • One-loop dilatation operator and the XXX spin chain

  • Coordinate and algebraic Bethe ansatz

  • Classical strings on AdS5×S5: giant magnons, BMN limit, finite-gap method

  • Asymptotic Bethe ansatz and the su(2|2) S-matrix

  • Dressing phase and crossing symmetry

References

  1. V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press, 1993.

  2. P. Di Francesco, P. Mathieu, and D. Sénéchal, Conformal Field Theory, Springer, 1997.

  3. O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri, and Y. Oz, “Large N Field Theories, String Theory and Gravity,” Phys. Rept.323 (2000) 183 [hep-th/9905111].

  4. E. D’Hoker and D. Z. Freedman, “Supersymmetric Gauge Theories and the AdS/CFT Correspondence,” TASI 2001 Lectures [hep-th/0201253].

  5. J. A. Minahan and K. Zarembo, “The Bethe ansatz for 𝒩=4 SYM,” JHEP0303 (2003) 013 [hep-th/0212208].

  6. O. Babelon, D. Bernard, and M. Talon, Introduction to Classical Integrable Systems, Cambridge University Press, 2003.

  7. N. Beisert, “The su(2|2) dynamic S-matrix,” Adv. Theor. Math. Phys.12 (2008) 945 [hep-th/0511082].

  8. D. Tong, Lectures on String Theory [arXiv:0908.0333].

  9. G. Arutyunov and S. Frolov, “Foundations of the AdS5×S5 Superstring. Part I,” J. Phys. A42 (2009) 254003 [arXiv:0901.4937].

  10. N. Beisert et al., “Review of AdS/CFT Integrability: An Overview,” Lett. Math. Phys.99 (2012) 3 [arXiv:1012.3982].

Schedule

[1] Mar 28, Sat

A crash course on the AdS/CFT correspondence and string theory

Plan

  • [2-5] Apr 4, 11, 18, 25

  • [6-9] May 9, 16, 23, 30 (no lecture on May 2)

  • [10] June 6


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